المؤلفون: Dai, Xiaoying, He, Lianhua, Zhou, Aihui

مصطلحات موضوعية: keyword:adaptive finite element method, keyword:elliptic partial differential equations, keyword:perturbation argument, keyword:boundary value problem, keyword:eigenvalue problem, keyword:convergence, keyword:nonlinear boundary value problem, keyword:nonlinear eigenvalue problem, msc:35J25, msc:35J60, msc:35P15, msc:35P30, msc:65N12, msc:65N25, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3204453; zbl:Zbl 1313.65300

الاتاحة: http://hdl.handle.net/10338.dmlcz/702893

المؤلفون: Belarbi, Abdelkader, Benchohra, Mouffak, Ouahab, Abdelghani

مصطلحات موضوعية: keyword:multiple solutions, keyword:Leggett-Williams fixed point theorem, keyword:nonlinear boundary value problem, keyword:integral boundary conditions, msc:34B10, msc:34B15, msc:34B18, msc:34B27, msc:47N20

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Relation: mr:MR2431225; zbl:Zbl 1212.34051; reference:[1] Agarwal, R. P., O’Regan, D.: Existence of three solutions to integral and discrete equations via the Leggett-Williams fixed point theorem.Rocky Mountain J. Math. 31 (2001), 23–35. Zbl 0979.45003, MR 1821365, 10.1216/rmjm/1008959665; reference:[2] Agarwal, R. P., O’Regan, D., Wong, P. J. Y.: Positive Solutions of Differential, Difference and Integral Equations.Kluwer Academic Publishers, Dordrecht, 1999. MR 1680024; reference:[3] Ahmad, B, Khan, R. A., Sivasundaram, S.: Generalized quasilinearization method for a first order differential equation with integral boundary condition.Dynam. Contin. Discrete Impuls. Systems, Ser. A Math. Anal. 12 (2005), 289–296. Zbl 1084.34007, MR 2170414; reference:[4] Anderson, D., Avery, R., Peterson, A.: Three positive solutions to a discrete focal boundary value problem. Positive solutions of nonlinear problems.J. Comput. Appl. Math. 88 (1998), 103–118. MR 1609058, 10.1016/S0377-0427(97)00201-X; reference:[5] Brykalov, S. A.: A second order nonlinear problem with two-point and integral boundary conditions.Georgian Math. J. 1 (1994), 243–249. Zbl 0807.34021, 10.1007/BF02254673; reference:[6] Denche, M., Marhoune, A. L.: High-order mixed-type differential equations with weighted integral boundary conditions.Electron. J. Differential Equations 60 (2000), 1–10. Zbl 0967.35101, MR 1787207; reference:[7] Gallardo, J. M.: Second-order differential operators with integral boundary conditions and generation of analytic semigroups.Rocky Mountain J. Math. 30 (2000), 265–1291. Zbl 0984.34014, MR 1810167; reference:[8] Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones.Academic Press, San Diego, 1988. Zbl 0661.47045, MR 0959889; reference:[9] Karakostas, G. L., Tsamatos, P. Ch.: Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems.Electron. J. Differential Equations 30 (2002), 17. Zbl 0998.45004, MR 1907706; reference:[10] Khan, R. A.: The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions.Electron. J. Qual. Theory Differ. Equ. 19 (2003), 15. Zbl 1055.34033, MR 2039793; reference:[11] Krall, A. M.: The adjoint of a differential operator with integral boundary condition.Proc. Amer. Math. Soc. 16 (1965), 738–742. MR 0181794, 10.1090/S0002-9939-1965-0181794-9; reference:[12] Leggett, R. W., Williams, L.R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces.Indiana Univ. Math. J. 28 (1979), 673–688. Zbl 0421.47033, MR 0542951, 10.1512/iumj.1979.28.28046; reference:[13] Lomtatidze, A., Malaguti, L.: On a nonlocal boundary value problem for second order nonlinear singular differential equations.Georgian Math. J. 7 (2000), 133–154. Zbl 0967.34011, MR 1768050

الاتاحة: http://hdl.handle.net/10338.dmlcz/108090

المؤلفون: Ma, De-xiang, Ge, Wei-Gao, Gui, Zhan-Ji

مصطلحات موضوعية: keyword:iteration, keyword:symmetric and monotone positive solution, keyword:nonlinear boundary value problem, keyword:$p$-Laplacian, msc:34A45, msc:34B10, msc:34B15, msc:34B18

وصف الملف: application/pdf

Relation: mr:MR2309955; zbl:Zbl 1174.34018; reference:[1] J. Wang: The existence of positive solutions for the one-dimensional $p$-Laplacian.Proc. Am. Math. Soc. 125 (1997), 2275–2283. Zbl 0884.34032, MR 1423340, 10.1090/S0002-9939-97-04148-8; reference:[2] L. Kong, J. Wang: Multiple positive solutions for the one-dimensional $p$-Laplacian.Nonlinear Analysis 42 (2000), 1327–1333. MR 1784078, 10.1016/S0362-546X(99)00143-1; reference:[3] D. Guo, V. Lakshmikantham: Nonlinear Problems in Abstract. Cones.Academic Press, Boston, 1988. MR 0959889; reference:[4] X. He, W. Ge: Twin positive solutions for the one-dimensional $p$-Laplacian.Nonlinear Analysis 56 (2004), 975–984. Zbl 1061.34013, MR 2038732, 10.1016/j.na.2003.07.022; reference:[5] R. I. Avery, C. J. Chyan, and J. Henderson: Twin solutions of boundary value problems for ordinary differential equations and finite difference equations.Comput. Math. Appl. 42 (2001), 695–704. MR 1838025, 10.1016/S0898-1221(01)00188-2; reference:[6] R. P. Agarwal, H. Lü and D. O’Regan: Eigenvalues and the one-dimensional $p$-Laplacian.J. Math. Anal. Appl. 266 (2002), 383–340. MR 1880513, 10.1006/jmaa.2001.7742; reference:[7] Y. Guo, W. Ge: Three positive solutions for the one-dimensional $p$-Laplacian.Nonlinear Analysis 286 (2003), 491–508. Zbl 1045.34005, MR 2008845; reference:[8] H. Amann: Fixed point equations and nonlinear eigenvalue problems in order Banach spaces.SIAM Rev. 18 (1976), 620–709. MR 0415432, 10.1137/1018114

الاتاحة: http://hdl.handle.net/10338.dmlcz/128161

المؤلفون: Staněk, Svatoslav

مصطلحات موضوعية: keyword:nonlinear boundary value problem, keyword:existence, keyword:lower and upper functions, keyword:$\alpha $-condensing operator, keyword:Borsuk antipodal theorem, keyword:Leray-Schauder degree, keyword:homotopy, msc:34B15, msc:47N20

وصف الملف: application/pdf

Relation: mr:MR1909594; zbl:Zbl 1087.34007; reference:[1] Cabada A., Pouso R. L.: Existence results for the problem $(\Phi (u^{\prime }))^{\prime }=f(t,u,u^{\prime })$ with nonlinear boundary conditions.Nonlinear Anal. 35 (1999), 221–231. MR 1643240; reference:[2] Deimling K.: Nonlinear Functional Analysis.Springer-Verlag, Berlin Heidelberg, 1985. Zbl 0559.47040, MR 0787404; reference:[3] Kiguradze I. T.: Boundary Value Problems for Systems of Ordinary Differential Equations.In “Current Problems in Mathematics: Newest Results", Vol. 30, 3–103, Moscow 1987 (in Russian); English transl.: J. Soviet Math. 43 (1988), 2340–2417. Zbl 0782.34025, MR 0925829; reference:[4] Kiguradze I. T., Lezhava N. R.: Some nonlinear two-point boundary value problems.Differentsial’nyie Uravneniya 10 (1974), 2147–2161 (in Russian); English transl.: Differ. Equations 10 (1974), 1660–1671. MR 0364733; reference:[5] Kiguradze I. T., Lezhava N. R.: On a nonlinear boundary value problem.Funct. theor. Methods in Differ. Equat., Pitman Publ. London 1976, 259–276. Zbl 0346.34008, MR 0499409; reference:[6] Staněk S.: Two-point functional boundary value problems without growth restrictions.Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 37 (1998), 123–142. Zbl 0963.34061, MR 1690481; reference:[7] Thompson H. B.: Second order ordinary differential equations with fully nonlinear two point boundary conditions.Pacific. J. Math. 172 (1996), 255–277. Zbl 0862.34015, MR 1379297; reference:[8] Thompson H. B.: Second order ordinary differential equations with fully nonlinear two point boundary conditions II.Pacific. J. Math. 172 (1996), 279–297. Zbl 0862.34015, MR 1379297; reference:[9] Wang M. X., Cabada A., Nieto J. J.: Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions.Ann. Polon. Math. 58 (1993), 221–235. Zbl 0789.34027, MR 1244394

الاتاحة: http://hdl.handle.net/10338.dmlcz/107827

المؤلفون: Borevich, E. Z., Chistyakov, V. M.

مصطلحات موضوعية: keyword:nonlinear boundary value problem, keyword:asymptotic behaviour of solutions, keyword:semiconductors, keyword:carrier transport, keyword:constant densities of ionized impurities, keyword:interior transition layer phenomena, msc:35B35, msc:35B40, msc:35D05, msc:35F20, msc:35Q20, msc:82D37

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Relation: mr:MR1925194; zbl:Zbl 1059.35026; reference:[1] L. Recke: An example for bifurcation of solutions of the basic equations for carrier distributions in semiconductors.Z. Angew. Math. Mech. 67 (1987), 269–271. Zbl 0625.34014, MR 0916259, 10.1002/zamm.19870670614; reference:[2] P. C. Fife: Boundary and interior transition layer phenomena for pairs of second-order differential equations.J. Math. Anal. Appl. 54 (1976), 497–521. Zbl 0345.34044, MR 0419961, 10.1016/0022-247X(76)90218-3; reference:[3] P. C. Fife: Transition Layers in Singular Perturbation Problems.J. Differential Equations 15 (1974), 77–105. Zbl 0259.34067, MR 0330665, 10.1016/0022-0396(74)90088-6; reference:[4] M. G. Crandall, P. H. Rabinowitz: Bifurcation from simple eigenvalues.J. Funct. Anal. 8 (1971), 321–340. MR 0288640; reference:[5] V. L. Bonch-Bruevich: Domain Electric Instability in Semiconductors.Nauka, Moskva, 1972. (Russian); reference:[6] P. H. Rabinowitz: Some global results for nonlinear eigenvalue problems.J. Funct. Anal. 7 (1971), 487–513. Zbl 0212.16504, MR 0301587; reference:[7] R. E. O’Malley jun.: Phase-plane solutions to some perturbation problems.J. Math. Anal. Appl. 54 (1976), 449–466. MR 0450722, 10.1016/0022-247X(76)90214-6; reference:[8] D. Henry: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics.Springer-Verlag, Berlin-Heidelberg-New York, 1981. MR 0610244; reference:[9] K. W. Chang, F. A. Howes: Nonlinear Singular Perturbation Phenomena: Theory and Applications.Springer-Verlag, New York, 1984. MR 0764395

الاتاحة: http://hdl.handle.net/10338.dmlcz/134474

المؤلفون: Švec, Marko

مصطلحات موضوعية: keyword:nonlinear boundary value problem, keyword:differential inclusion, keyword:measurable selector, keyword:Ky Fan’s fixed point theorem, msc:34A60, msc:34B15, msc:34C25, msc:47J05, msc:47N20

وصف الملف: application/pdf

Relation: mr:MR1464311; zbl:Zbl 0914.34015; reference:[1] Y. Kitamura: On nonoscillatory solutions of functional differential equations with a general deviating argument.Hiroshima Math. J. 8 (1978), 49-62. Zbl 0387.34048, MR 0466865

الاتاحة: http://hdl.handle.net/10338.dmlcz/107607

المؤلفون: Liu, Liping, Křížek, Michal, Neittaanmäki, Pekka

مصطلحات موضوعية: keyword:nonlinear boundary value problem, keyword:finite elements, keyword:rate of convergence, keyword:anisotropic heat conduction, msc:35J65, msc:65N30, msc:74A15

وصف الملف: application/pdf

Relation: mr:MR1415252; zbl:Zbl 0870.65096; reference:[1] L. Boccardo, T. Gallouët and F. Murat: Unicité de la solution de certaines équations elliptiques non linéaires.C. R. Acad. Sci. Paris Ser. I Math. 315 (1992), 1159–1164. MR 1194509; reference:[2] Z. Chen: On the existence, uniqueness and convergence of nonlinear mixed finite element methods.Mat. Apl. Comput. 8 (1989), 241–258. Zbl 0709.65080, MR 1067288; reference:[3] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174; reference:[4] J. Douglas and T. Dupont: A Galerkin method for a nonlinear Dirichlet problem.Math. Comp. 29 (1975), 689–696. MR 0431747, 10.1090/S0025-5718-1975-0431747-2; reference:[5] J. Douglas, T. Dupont and J. Serrin: Uniqueness and comparison theorems for nonlinear elliptic equations in divergence form.Arch. Rational Mech. Anal. 42 (1971), 157–168. MR 0393829, 10.1007/BF00250482; reference:[6] M. Feistauer, M. Křížek and V. Sobotíková: An analysis of finite element variational crimes for a nonlinear elliptic problem of a nonmonotone type.East-West J. Numer. Math. 1 (1993), 267–285. MR 1318806; reference:[7] M. Feistauer and V. Sobotíková: Finite element approximation of nonlinear elliptic problems with discontinuous coefficients.RAIRO Modèl. Math. Anal. Numér. 24 (1990), 457–500. MR 1070966, 10.1051/m2an/1990240404571; reference:[8] M. Feistauer and A. Ženíšek: Compactness method in finite element theory of nonlinear elliptic problems.Numer. Math. 52 (1988), 147–163. MR 0923708, 10.1007/BF01398687; reference:[9] J. Franců: Weakly continuous operators. Applications to differential equations.Appl. Math. 39 (1994), 45–56. MR 1254746; reference:[10] J. Frehse and R. Rannacher: Asymptotic $L^\infty $-error estimates for linear finite element approximations of quasilinear boundary value problems.SIAM J. Numer. Anal. 15 (1978), 418–431. MR 0502037, 10.1137/0715026; reference:[11] D. Gilbarg and N. S. Trudinger: Elliptic Partial Differential Equations of Second Order.Springer-Verlag, Berlin, 1977. MR 0473443; reference:[12] I. Hlaváček: Reliable solution of a quasilinear nonpotential elliptic problem of a nonmonotone type with respect to the uncertainty in coefficients.accepted by J. Math. Anal. Appl. MR 1464890; reference:[13] I. Hlaváček and M. Křížek: On a nonpotential and nonmonotone second order elliptic problem with mixed boundary conditions.Stability Appl. Anal. Contin. Media 3 (1993), 85–97.; reference:[14] I. Hlaváček, M. Křížek and J. Malý: On Galerkin approximations of quasilinear nonpotential elliptic problem of a nonmonotone type.J.Math. Anal. Appl. 184 (1994), 168–189. MR 1275952, 10.1006/jmaa.1994.1192; reference:[15] M. Křížek and Q. Lin: On diagonal dominance of stiffness matrices in 3D.East-West J. Numer. Math. 3 (1995), 59–69. MR 1331484; reference:[16] M. Křížek and L. Liu: On a comparison principle for a quasilinear elliplic boundary value problem of a nonmonotone type.Applicationes Mathematicae 24 (1996), 97–107. MR 1404987, 10.4064/am-24-1-97-107; reference:[17] M. Křížek and P. Neittaanmäki: Mathematical and Numerical Modelling in Electrical Engineering: Theory and Applications.Kluwer, Dordrecht, 1996. MR 1431889; reference:[18] M. Křížek and V. Preiningerová: 3d solution of temperature fields in magnetic circuits of large transformers (in Czech).Elektrotechn. obzor 76 (1987), 646–652.; reference:[19] F. A. Milner: Mixed finite element methods for quasilinear second-order elliptic problems.Math. Comp. 44 (1985), 303–320. Zbl 0567.65079, MR 0777266, 10.1090/S0025-5718-1985-0777266-1; reference:[20] J. Nečas: Les Méthodes Directes en Théorie des Équations Elliptiques.Academia, Prague, 1967. MR 0227584; reference:[21] J. Nečas: Introduction to the Theory of Nonlinear Elliptic Equations.Teubner, Leipzig, 1983. MR 0731261; reference:[22] J. A. Nitsche: On $L_\infty $-convergence of finite element approximations to the solution of nonlinear boundary value problem.in: Proc. of Numer. Anal. Conf. (ed. J. H. Miller), Academic Press, New York, 1977, 317–325. MR 0513215; reference:[23] R. H. Nochetto: Introduzione al Metodo Degli Elementi Finiti.Lecture Notes, Trento Univ., 1985.; reference:[24] V. Preiningerová, M. Křížek and V. Kahoun: Temperature distribution in large transformer cores.Proc. of GANZ Conf. (ed. M. Franyó), Budapest, 1985, 254–261.; reference:[25] K. Yosida: Functional Analysis.Springer-Verlag, Berlin, 1965. Zbl 0126.11504; reference:[26] A. Ženíšek: Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations.Academic Press, London, 1990. MR 1086876; reference:[27] A. Ženíšek: The finite element method for nonlinear elliptic equations with discontinuous coeffcients.Numer. Math. 58 (1990), 51–77. 10.1007/BF01385610

الاتاحة: http://hdl.handle.net/10338.dmlcz/134338

المؤلفون: Sibony, Moïse

مصطلحات موضوعية: keyword:nonlinear operator equations in Hilbert space, keyword:iterative methods, keyword:numerical methods, keyword:nonlinear boundary value problem for elliptic equations, keyword:numerical example, msc:35J05, msc:35J60, msc:47J25, msc:65J15, msc:65N10, msc:65N99

وصف الملف: application/pdf

Relation: mr:MR0451763; zbl:Zbl 0407.65024; reference:[1] H. Brezis: Equations et inéquations non linéaires dans les espaces vectoriels en dualité.Annales Inst. Fourier, Tome XVIII, Fasc. 1, 1968, p. 115-175. Zbl 0169.18602, MR 0270222, 10.5802/aif.280; reference:[2] H. Brezis, M. Sibony: Méthodes d'approximations et d'iterations pour les opérateurs monotones.Archive for Rational Mechanics and Analysis, t. 28, (1968), p. 59-82. MR 0220110, 10.1007/BF00281564; reference:[3] F. Browder: Problèmes non linéaires.Université de Montreal, 1966. Zbl 0153.17302; reference:[4] F. Browder: Existence theorems of non linear partial differential equations.Proc. Amer. Math. Soc., 1968, Summer Institue in Global Analysis.; reference:[5] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod Gauthier-Villars, 1969. Zbl 0189.40603, MR 0259693; reference:[6] M. Sibony: Sur l'approximation d'équations et inéquations aux dérivées partielles non linéaires de type monotone.J. of Math. Anal, and Appl. Vol. 34, n° 3, June 1971, p. 502-564. MR 0420361, 10.1016/0022-247X(71)90095-3; reference:[7] M. Sibony: Méthodes itératives sur les équations et inéquations aux dérivées partielles non linéaires de type monotone.Calcolo, Vol. 7, Fasc. 1 - 2, 1970, p. 65-183. MR 0659098, 10.1007/BF02575559

الاتاحة: http://hdl.handle.net/10338.dmlcz/103704