Symmetric positive solutions of fourth order integral BVP for an increasing homeomorphism and homomorphism with sign-changing nonlinearity on time scales

In this paper, we consider the eigenvalue problems for fourth order integral boundary value problems on time scales for an increasing homeomorphism and homomorphism with sign changing nonlinearities. By using a fixed point index theorem, we give the existence of eigenvalue intervals in which there exist one symmetric positive solution to the problem. An example is also given to demonstrate the main results.