المؤلفون: Papageorgiou, Nikolaos S., Papalini, Francesca

مصطلحات موضوعية: keyword:one dimensional $p$-Laplacian, keyword:maximal monotone operator, keyword:pseudomonotone operator, keyword:generalized pseudomonotonicity, keyword:coercive operator, keyword:first nonzero eigenvalue, keyword:upper solution, keyword:lower solution, keyword:truncation map, keyword:penalty function, keyword:multiplicity result, msc:34A36, msc:34B15, msc:34C25

وصف الملف: application/pdf

Relation: mr:MR1942658; zbl:Zbl 1090.34013; reference:[1] Ahmad S., Lazer A.: Critical point theory and a theorem of Amaral and Pera.Bollettino U.M.I. 6 (1984), 583–598. Zbl 0603.34036, MR 0774464; reference:[2] Boccardo L., Drábek P., Giacchetti D., Kučera M.: Generalization of Fredholm alternative for some nonlinear boundary value problem.Nonlinear Anal. T.M.A. 10 (1986), 1083–1103. MR 0857742; reference:[3] Dang H., Oppenheimer S. F.: Existence and uniqueness results for some nonlinear boundary value problems.J. Math. Anal. Appl. 198 (1996), 35–48. MR 1373525; reference:[4] Del Pino M., Elgueta M., Manasevich R.: A homotopic deformation along p of a Leray Schauder degree result and existence for $(%7C u^{\prime } %7C^{p-2}u^{\prime })^{\prime }+ f(t,u)=0, u(0)=u(T)=0, p1^*$.J. Differential Equations 80 (1989), 1–13. Zbl 0708.34019, MR 1003248; reference:[5] Del Pino M., Manasevich R., Murua A.: Existence and multiplicity of solutions with prescribed period for a second order quasilinear o.d.e.Nonlinear Anal. T.M.A. 18 (1992), 79–92. Zbl 0761.34032, MR 1138643; reference:[6] Drábek P.: Solvability of boundary value problems with homogeneous ordinary differential operator.Rend. Istit. Mat. Univ. Trieste 8 (1986), 105–124. MR 0928322; reference:[7] Fabry C., Fayyad D.: Periodic solutions of second order differential equations with a $p$-Laplacian and asymmetric nonlinearities.Rend. Istit. Mat. Univ. Trieste 24 (1992), 207–227. Zbl 0824.34026, MR 1310080; reference:[8] Fabry C., Mawhin J., Nkashama M. N.: A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations.Bull. London Math. Soc. 18 (1986), 173–180. Zbl 0586.34038, MR 0818822; reference:[9] Fonda A., Lupo D.: Periodic solutions of second order ordinary differential differential equations.Bollettino U.M.I. 7 (1989), 291–299. MR 1026756; reference:[10] Gilbarg D., Trudinger N.: Elliptic Partial Differential Equations of Second Order.Springer-Verlag, New York (1977). Zbl 0361.35003, MR 0473443; reference:[11] Gossez J.-P., Omari P.: A note on periodic solutions for second order ordinary differential equation.Bollettino U.M.I. 7 (1991), 223–231.; reference:[12] Guo Z.: Boundary value problems of a class of quasilinear differential equations.Diff. Integral Equations 6 (1993), 705–719. MR 1202567; reference:[13] Hu S., Papageorgiou N. S.: Handbook of Multivalued Analysis, Volume I: Theory.Kluwer, Dordrecht, The Netherlands (1997). Zbl 0887.47001, MR 1485775; reference:[14] Hu S., Papageorgiou N. S.: Handbook of Multivalued Analysis, Volume II: Applications.Kluwer, Dordrecht, The Netherlands (2000). Zbl 0943.47037, MR 1741926; reference:[15] Kesavan S.: Topics in Functional Analysis and Applications.Wiley, New York (1989). Zbl 0666.46001, MR 0990018; reference:[16] Manasevich R., Mawhin J.: Periodic solutions for nonlinear systems with $p$-Laplacian like operators.J. Differential Equations 145 (1998), 367–393. MR 1621038; reference:[17] Mawhin J., Willem M.: Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations.J. Differential Equations 2 (1984), 264–287. Zbl 0557.34036, MR 0741271; reference:[18] Zeidler E.: Nonlinear Functional Analysis and its Applications II.Springer-Verlag, New York (1985). MR 0768749

الاتاحة: http://hdl.handle.net/10338.dmlcz/107842

المؤلفون: Papageorgiou, Nikolaos S., Yannakakis, Nikolaos

مصطلحات موضوعية: keyword:multiple solutions, keyword:periodic problem, keyword:one-dimensional $p$-Laplacian, keyword:discontinuous vector field, keyword:nonsmooth Palais-Smale condition, keyword:locally Lipschitz function, keyword:generalized subdifferential, keyword:critical point, keyword:Saddle Point Theorem, keyword:Ekeland variational principle, msc:34A36, msc:34B15, msc:34C25, msc:47J30

وصف الملف: application/pdf

Relation: mr:MR1921589; zbl:Zbl 1090.34035; reference:[1] Boccardo L., Drábek P., Giachetti D., Kučera M.: Generalization of Fredholm alternative for nonlinear differential operators.Nonlinear Anal. 10 (1986), 1083–1103. MR 0857742; reference:[2] Chang K. C.: Variational methods for non-differentiable functionals and their applications to partial differential equations.J. Math. Anal. Appl. 80 (1981), 102–129. Zbl 0487.49027, MR 0614246; reference:[3] Clarke F. H.: Optimization and Nonsmooth Analysis.Wiley, New York 1983. Zbl 0582.49001, MR 0709590; reference:[4] Dang H., Oppenheimer S. F.: Existence and uniqueness results for some nonlinear boundary value problems.J. Math. Anal. Appl. 198 (1996), 35–48. MR 1373525; reference:[5] De Coster C.: On pairs of positive solutions for the one dimensional $p$-Laplacian.Nonlinear Anal. 23 (1994), 669–681. MR 1297285; reference:[6] Del Pino M., Elgueta M., Manasevich R.: A homotopic deformation along p of a Leray-Schauder degree result and existence for $(%7Cu^{\prime }%7C^{p-2}u^{\prime })^{\prime }+f(t,u)=0,\;u(0)=u(T)=0$.J. Differential Equations 80 (1989), 1–13. Zbl 0708.34019, MR 1003248; reference:[7] Del Pino M., Manasevich R., Murua A.: Existence and multiplicity of solutions with prescribed period for a second order quasilinear ode.Nonlinear Anal. 18 (1992), 79–92. MR 1138643; reference:[8] Drábek P., Invernizzi S.: On the periodic bvp for the forced Duffing equation with jumping nonlinearity.Nonlinear Anal. 10 (1986), 643–650. Zbl 0616.34010, MR 0849954; reference:[9] Fabry C., Fayyad D.: Periodic solutions of second order differential equations with a $p$-Laplacian and assymetric nonlinearities.Rend. Istit. Mat. Univ. Trieste 24 (1992), 207–227. MR 1310080; reference:[10] Fabry C., Mawhin J., Nkashama M.: A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations.Bull. London Math. Soc. 18 (1986), 173–180. Zbl 0586.34038, MR 0818822; reference:[11] Guo Z.: Boundary value problems of a class of quasilinear ordinary differential equations.Differential Integral Equations 6 (1993), 705–719. Zbl 0784.34018, MR 1202567; reference:[12] Hu S., Papageorgiou N. S.: Handbook of Multivalued Analysis. Vol I: Theory.Kluwer, The Netherlands, 1997. MR 1485775; reference:[13] Hu S., Papageorgiou N. S.: Handbook of Multivalued Analysis. Vol II: Applications.Kluwer, The Netherlands, 2000. MR 1741926; reference:[14] Manasevich R., Mawhin J.: Periodic solutions for nonlinear systems with $p$-Laplacian-like operators.J. Differential Equations 145 (1998), 367–393. MR 1621038; reference:[15] Papageorgiou N. S., Yannakakis N.: Nonlinear boundary value problems.Proc. Indian Acad. Sci. Math. Sci. 109 (1999), 211–230. Zbl 0952.34035, MR 1687731; reference:[16] Szulkin A.: Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems.Ann. Inst. H. Poincarè Non Linèaire 3 (1986), 77–109. Zbl 0612.58011, MR 0837231; reference:[17] Tang C.-L.: Existence and multiplicity of periodic solutions for nonautonomous second order systems.Nonlinear Anal. 32 (1998), 299–304. Zbl 0949.34032, MR 1610641; reference:[18] Zhang M.: Nonuniform nonresonance at the first eigenvalue of the $p$-Laplacian.Nonlinear Anal. 29 (1997), 41–51. Zbl 0876.35039, MR 1447568; reference:[19] Mawhin J. M., Willem M.: Critical Point Theory and Hamiltonian Systems.Springer, Berlin (1989). Zbl 0676.58017, MR 0982267

الاتاحة: http://hdl.handle.net/10338.dmlcz/107831