Existence of Three Positive Solutions to Some $p$-Laplacian Boundary Value Problems

TL;DR

This paper establishes conditions for the existence of at least three positive solutions to certain $p$-Laplacian boundary value problems on time scales using the Leggett-Williams fixed point theorem.

Contribution

It introduces new sufficient conditions for multiple positive solutions to $p$-Laplacian problems on time scales, expanding previous results.

Findings

At least three positive solutions exist under specified conditions.

Conditions are derived using Leggett-Williams fixed point theorem.

Results apply to boundary value problems on time scales.

Abstract

We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some $p$-Laplacian boundary value problems on time scales.