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.
Highlights
1 Introduction The theory of time scales was introduced by Stefan Hilger [ ] in his PhD thesis in in order to unify continuous and discrete analysis
There have been extensive studies on a boundary value problem (BVP) with signchanging nonlinearity on time scales by using the fixed point theorem on cones
In [ ], Feng, Pang and Ge discussed the existence of triple symmetric positive solutions by applying the fixed point theorem of functional type in a cone
Summary
The theory of time scales was introduced by Stefan Hilger [ ] in his PhD thesis in in order to unify continuous and discrete analysis. By using four functionals fixed point theorem [ ], we establish the existence of at least one symmetric positive solution for BVP To the best of our knowledge, symmetric positive solutions for multipoint BVP for an increasing homeomorphism and homomorphism with sign-changing nonlinearity on time scales by using four functionals fixed point theorem [ ] have not been considered till now. If y ∈ Cld[ , ]T is nonnegative on [ , ]T and y(t) ≡ on any subinterval of [ , ]T, the unique solution x(t) of BVP If y(t) ∈ Cld[ , ]T is symmetric nonnegative on [ , ]T and y(t) ≡ on any subinterval of [ , ]T, the unique solution x(t) of
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