Existence of sign-changing solutions for a third-order boundary value problem with nonlocal conditions of integral type
DOI:
https://doi.org/10.12775/TMNA.2022.074Keywords
Third-order nonlinear boundary value problems, integral boundary condition, existence of sign-changing solutions, Green’s function, Leray-Schauder Continuation PrincipleAbstract
We prove the existence of at least one sign-changing solution for a third-order nonlocal boundary value problem by applying Leray-Schauder Continuation Principle. To illustrate the applicability of the obtained results, we consider an example.References
A. Cabada, G. Infante and F.A.F. Tojo, Nonzero solutions of perturbed Hammerstein integral equations with deviated arguments and applications, Topol. Methods Nonlinear Anal. 47 (2016), no. 1, 265–287.
Q.A. Dang and Q.L. Dang, A unified approach to fully third order nonlinear boundary value problems, J. Nonlinear Funct. Anal. 2020 (2020), ID 9, 1–17.
R. Dhanya, R. Shivaji and B. Son, A three solution theorem for a singular differential equation with nonlinear boundary conditions, Topol. Methods Nonlinear Anal. 54 (2019), no. 2A, 445–457.
J.R. Graef and J.R.L. Webb, Third order boundary value problems with nonlocal boundary conditions, Nonlinear Anal. 71 (2009), 1542–1551.
B. Hopkins and N. Kosmatov, Third-order boundary value problems with sign-changing solutions, Nonlinear Anal. 67 (2007), 126–137.
G. Infante, Nonzero positive solutions of a multi-parameter elliptic system with functional bcs, Topol. Methods Nonlinear Anal. 52 (2018), no. 2, 665–675.
G. Infante, Nontrivial solutions of systems of perturbed Hammerstein integral equations with functional terms, Mathematics 9 (2021), no. 4, 330.
P.S. Kelevedjiev and T.Z. Todorov, Existence of solutions of nonlinear third-order two-point boundary value problems, Electron. J. Qual. Theory Differ. Equ. 23 (2019), 1–15.
Y. Niu and B Yan, The existence of positive solutions for the singular two-point boundary value problem, Topol. Methods Nonlinear Anal. 49 (2017), no. 2, 665–682.
A. Sfecci, Double resonance in Sturm–Liouville planar boundary value problems, Topol. Methods Nonlinear Anal. 55 (2020), no. 2, 655–680.
J.R.L. Webb, Non-local second-order boundary value problems with derivative-dependent nonlinearity, Philos. Trans. Roy. Soc. A 379 (2021), 1–12.
J.R.L. Webb and G. Infante, Nonlocal boundary value problems of arbitrary order J. London Math. Soc. 79 (2009), no. 1, 238–258.
J.R.L. Webb and G. Infante, Positive solutions of nonlocal boundary value problems involving integral conditions NoDEA Nonlinear Differential Equations Appl. 15 (2008), 45–67.
P. Wu and Y. Zhou, Sign-changing solutions for the boundary value problem involving the fractional p-Laplacian, Topol. Methods Nonlinear Anal. 57 (2021), no. 2, 597–619.
E. Zeidler, Nonlinear Functional Analysis and its Applications I. Fixed-Point Theorems, Springer–Verlag, New York, 1986.
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