Some existence results on positive solutions for an iterative second-order boundary-value problem with integral boundary conditions
DOI:
https://doi.org/10.5269/bspm.52461Abstract
The present paper is devoted to study a nonlinear second order differential equation with iterative source term and integral boundary conditions. The utilization of some suitable fixed point theorems ultimately led us to establish some sufficient conditions that guarantee the existence, uniqueness and continuous dependence of positive bounded solutions. The obtained results are illustrated by an example.
References
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11. J. Galvis, E. M. Rojas, A. V. Sinitsyn, Existence of positive solutions of a nonlinear second-order boundary-value problem with integral boundary conditions, Electron. J. Differential Equations, 236(2015), 1−7.
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15. E. Zeidler, Nonlinear functional analysis and its applications, fixed-point theorems, Springer-Verlage, Berlin, 1993.
16. H. Y. Zhao, J. Liu, Periodic Solutions of a Second-Order Functional Differential Equation with State-Dependent Argument, Mediterr. J. Math. 15(2018), p.p 1−15. https://doi.org/10.1007/s00009-018-1261-2
2. C. Babbage, An essay towards the calculus of functions, Philos. Trans. R. Soc. Lond, 105 (1815), 389-432. https://doi.org/10.1098/rstl.1815.0024
3. Z. Bekri, S. Benaicha, Existence of Solution for Nonlinear Fourth-order Three-point Boundary Value Problem, Bol. Soc. Paran. Mat, 38 1 (2020): 67−82. https://doi.org/10.5269/bspm.v38i1.34767
4. M. Benchohra, J. J. Nieto, A. Ouahab, Second-order boundary value problem with integral boundary conditions, Bound. Value Probl, 1 (2011), 260−309. https://doi.org/10.1155/2011/260309
5. A. Bouakkaz, A. Ardjouni, A. Djoudi, Periodic Solutions for a Nonlinear Iterative Functional Differential Equation, Electron. J. Math. Anal. Appl, Vol. 7(2019), 156−166.
6. A. Bouakkaz, A. Ardjouni, A. Djoudi, Periodic Solutions for a Second Order Nonlinear Functional Differential Equation with Iterrative Terms by Schauder Fixed Point Theorem, Acta Math. Univ. Comenian, LXXXV II (2018), 223 − 235.
7. A. Bouakkaz, A. Ardjouni, R. Khemis, A. Djoudi, Periodic solutions of a class of third-order functional differential equations with iterative source terms, Bol. Soc. Mat. Mexicana (3), https://doi.org/10.1007/s40590-019-00267-x
8. A. Boucherif, Second-order boundary value problems with integral boundary conditions, Nonlinear Anal, 70(2009), 364−371. https://doi.org/10.1016/j.na.2007.12.007
9. J. Cannon, The solution of the heat equation subject to the specification of energy, Quart. Appl. Math, 21(1963), 155−160. https://doi.org/10.1090/qam/160437
10. R. Chegis, Numerical solution of a heat conduction problem with an integral boundary condition, Litovsk. Mat. Sb, 24(1984), 209−215.
11. J. Galvis, E. M. Rojas, A. V. Sinitsyn, Existence of positive solutions of a nonlinear second-order boundary-value problem with integral boundary conditions, Electron. J. Differential Equations, 236(2015), 1−7.
12. G. Infante, Positive solutions of nonlocal boundary value problems with singularities, Discrete Contin. Dyn. Syst, 2009, 377−384.
13. N. Ionkin, Solution of a boundary value problem in heat conduction theory with nonlocal boundary conditions, Differ. Equ, 13(1977), 294−304.
14. V. R. Petuhov, On a boundary value problem, (Russian. English summary), Trudy Sem. Teor. Differencial. Uravneniıs Otklon. Argumentom Univ. Druzby Narodov Patrisa Limumby, 3(1965), 252−2.
15. E. Zeidler, Nonlinear functional analysis and its applications, fixed-point theorems, Springer-Verlage, Berlin, 1993.
16. H. Y. Zhao, J. Liu, Periodic Solutions of a Second-Order Functional Differential Equation with State-Dependent Argument, Mediterr. J. Math. 15(2018), p.p 1−15. https://doi.org/10.1007/s00009-018-1261-2
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2022-02-04
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