Existence, multiplicity and infinite solvability of positive solutions for $p$-Laplacian dynamic equations on time scales

Abstract

In this paper, by using Guo-Krasnosel'skii fixed point theorem in cones, we study the existence, multiplicity and infinite solvability of positive solutions for the following three-point boundary value problems for $p$-Laplacian dynamic equations on time scales $$displaylines{ [ Phi _p(u^{riangle }(t))] ^{riangledown}+a(t)f(t,u(t)) =0,quad tin [0,T]_{mathbf{T}}, cr u(0)-B_0(u^{riangle }(eta )) = 0,quad u^{riangle }(T)=0. }$$ By multiplicity we mean the existence of arbitrary number of solutions.

Keywords

• Time scales
• $p$-Laplacian
• boundary value problem
• positive solution
• existence
• multiplicity
• infinite solvability.