Existence of Positive Solutions for m‐Point Boundary Value Problems on Time Scales

Abstract

We study the one-dimensional p-Laplacian m-point boundary value problemsome new results are obtained for the existence of at least one, two, and three positive solution/solutions of the above problem by using Krasnosel skll s fixed point theorem, new fixed point theorem due to Avery and Henderson, as well as Leggett-Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian mpoint boundary value problem on time scales has been studied.

Existence of Three Positive Solutions to Somep-Laplacian Boundary Value Problems

“…In contrast with our previous works [17,18], which make use of the �rasnoselskii �xed point theorem and the �xed point index theory, respectively, here we use the Leggett-Williams �xed point theorem [20,21] obtaining multiplicity of positive solutions. e application of the Leggett-Williams �xed point theorem for proving multiplicity of solutions for boundary value problems on time scales was �rst introduced by Agarwal and O'Regan [22] and is now recognized as an important tool to prove existence of positive solutions for boundary value problems on time scales [23][24][25][26][27][28].…”