Infinite solutions having a prescribed number of nodes for a p-Laplacian problem

TL;DR

This paper proves the existence of infinitely many solutions with prescribed nodes for a p-Laplacian problem under weaker nonlinear assumptions, providing a new proof and characterizing critical values of radial solutions.

Contribution

It introduces a novel proof technique for infinite solutions with prescribed nodes under weaker conditions on the nonlinearity.

Findings

Existence of infinitely many solutions with prescribed nodes.

Weaker super-quadratic conditions suffice for solution multiplicity.

Global characterization of critical values of nodal radial solutions.

Abstract

In this paper, we are concern with the multiplicity of solutions for a p-Laplacian problem. A weaker super-quadratic assumptions is required on the nonlinearity. Under the weaker condition we give a new proof for the infinite solutions having a prescribed number of nodes to the problem. It turns out that the weaker condition on nonlinearity suffices to guarantee the infinitely many solutions. At the same time, a global characterization of the critical values of the nodal radial solutions are given.