Multiple Positive solutions of a $(p_1,p_2)$-Laplacian system with nonlinear BCs

TL;DR

This paper investigates the existence and multiplicity of positive solutions for a coupled $(p_1,p_2)$-Laplacian system with nonlinear boundary conditions using fixed point index theory, providing theoretical results and illustrative examples.

Contribution

It introduces new conditions for positive solutions of a $(p_1,p_2)$-Laplacian system with nonlinear boundary conditions, expanding existing mathematical frameworks.

Findings

Established criteria for existence and non-existence of solutions

Identified conditions for multiple positive solutions

Provided an example illustrating the theoretical results

Abstract

Using the theory of fixed point index, we discuss existence, non-existence, localization and multiplicity of positive solutions for a $(p_1,p_2)$-Laplacian system with nonlinear Robin and/or Dirichlet type boundary conditions. We give an example to illustrate our theory.