Academic Journal
On a singular multi-point third-order boundary value problem on the half-line
| العنوان: | On a singular multi-point third-order boundary value problem on the half-line |
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| المؤلفون: | Benbaziz, Zakia, Djebali, Smail |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 2020 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:singular nonlinear boundary value problem, keyword:positive solution, keyword:Krasnosel'skii fixed point theorem, keyword:multi-point, keyword:half-line, msc:34B10, msc:34B16, msc:34B18, msc:34B40 |
| الوصف: | summary:We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel'skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity $f=f(t,x,y)$ which satisfies upper and lower-homogeneity conditions in the space variables $x, y$ may be also singular at time $t=0$. Two examples of applications are included to illustrate the existence theorems. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0862-7959 2464-7136 |
| Relation: | mr:MR4221836; zbl:07250712; reference:[1] Agarwal, R. P., O'Regan, D.: Infinite Interval Problems for Differential, Difference and Integral Equations.Kluwer Academic Publishers, Dordrecht (2001). Zbl 0988.34002, MR 1845855, 10.1007/978-94-010-0718-4; reference:[2] Chen, S., Zhang, Y.: Singular boundary value problems on a half-line.J. Math. Anal. Appl. 195 (1995), 449-468. Zbl 0852.34019, MR 1354555, 10.1006/jmaa.1995.1367; reference:[3] Corduneanu, C.: Integral Equations and Stability of Feedback Systems.Mathematics in Science and Engineering 104. Academic Press, New York (1973). Zbl 0273.45001, MR 0358245, 10.1016/s0076-5392(08)x6099-0; reference:[4] Djebali, S., Mebarki, K.: Multiple positive solutions for singular BVPs on the positive half-line.Comput. Math. Appl. 55 (2008), 2940-2952. Zbl 1142.34316, MR 2401442, 10.1016/j.camwa.2007.11.023; reference:[5] Djebali, S., Saifi, O.: Third order BVPs with $\phi$-Laplacian operators on $[0,+\infty)$.Afr. Diaspora J. Math. 16 (2013), 1-17. Zbl 1283.34019, MR 3091711; reference:[6] Guo, D. J., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones.Notes and Reports in Mathematics in Science and Engineering 5. Academic Press, Boston (1988). Zbl 0661.47045, MR 0959889, 10.1016/c2013-0-10750-7; reference:[7] Liang, S., Zhang, J.: Positive solutions for singular third-order boundary value problem with dependence on the first order derivative on the half-line.Acta Appl. Math. 111 (2010), 27-43. Zbl 1203.34038, MR 2653048, 10.1007/s10440-009-9528-z; reference:[8] Liu, Y.: Existence and unboundedness of positive solutions for singular boundary value problems on half-line.Appl. Math. Comput. 144 (2003), 543-556. Zbl 1036.34027, MR 1994092, 10.1016/S0096-3003(02)00431-9; reference:[9] Wei, Z.: A necessary and sufficient condition for the existence of positive solutions of singular super-linear $m$-point boundary value problems.Appl. Math. Comput. 179 (2006), 67-78. Zbl 1166.34305, MR 2260858, 10.1016/j.amc.2005.11.077; reference:[10] Wei, Z.: Some necessary and sufficient conditions for existence of positive solutions for third order singular super-linear multi-point boundary value problems.J. Appl. Math. Comput. 46 (2014), 407-422. Zbl 1311.34052, MR 3252121, 10.1007/s12190-014-0756-7; reference:[11] Yan, B., O'Regan, D., Agarwal, R. P.: Unbounded positive solutions for second order singular boundary value problems with derivative dependence on infinite intervals.Funkc. Ekvacioj, Ser. Int. 51 (2008), 81-106. Zbl 1158.34011, MR 2427544, 10.1619/fesi.51.81 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/148351 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.1A11B8B5 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 08627959 24647136 |
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