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

Fatma Tokmak and Ilkay Yaslan Karaca*

Author Affiliations

Department of Mathematics, Ege University, Bornova, Izmir, 35100, Turkey

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Boundary Value Problems 2013, 2013:52  doi:10.1186/1687-2770-2013-52

Published: 14 March 2013


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.

symmetric positive solution; fixed-point theorem; time scales; m-point boundary value problem; increasing homeomorphism and homomorphism