Multiple positive pseudo-symmetric solutions of p-Laplacian dynamic equations on time scales

Abstract

Let T be a pseudo-symmetric time scale such that 0 , T ∈ T . We consider a three-point boundary value problem for p -Laplacian dynamic equations on time scales T . Some new sufficient conditions are obtained for the existence of at least single, twin, triple or arbitrary odd positive pseudo-symmetric solutions of this problem by using pseudo-symmetric technique and fixed-point theorems in cone. Our results generalize and improve the results in paper by Su et al. [Y.H. Su, W.T. Li, H.R. Sun, Triple positive pseudo-symmetric solutions of three-point BVPs for p -Laplacian dynamic equations on time scales, Nonlinear Anal. TMA 68 (2008) 1442–1452]. As applications, three examples are given to illustrate the main results and their differences. These results are new for the special cases of continuous and discrete equations, as well as in the general time scale setting.