Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales

Abstract

In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that the considered equation admits a nonlinear term f whose sign is allowed to change. The discussed problem involves both an increasing homeomorphism and homomorphism, which generalizes the p-Laplacian operator. An example which supports our theoretical results is also indicated. MSC: 34B10; 39A10

Positive solutions of nth-order m-point impulsive boundary value problems

“…Since then, nonlinear second-order multipoint boundary value problems have been studied by quite a number of authors. We refer the reader to [9,16,17,19,21,25] and the references therein. On the other hand, there are fewer results in the literature on multi-point boundary value problems for higher-order di erential equations, see [6,8,13,23].…”

Multi-parameter second-order impulsive indefinite boundary value problems

“…It is well accepted that fixed point theorems in cones have been instrumental in showing the existence, multiplicity of positive solutions of various boundary value problems for differential equations. See, for instance, [39][40][41][42][43][44][45][46] and the references therein. In this paper, we will use Krasnoselskii's fixed point theorem in a cone to investigate the existence and multiplicity of positive solutions of problem (1.1).…”

Existence of positive solutions for fourth‐order impulsive integral boundary value problems on time scales

“…The study unifies the existing results in differential and finite difference equations and provides new powerful tools for exploring connections between the traditionally separated fields. For further information concerning the theory and applications dynamic equations on time scales, we refer the reader to the books [4,5] and the papers [6][7][8][9][10][11][12].…”