Increasing radial solutions for Neumann problems without growth restrictions

TL;DR

This paper proves the existence of positive increasing radial solutions for superlinear Neumann problems in a ball without growth restrictions on the nonlinearity, using topological and variational methods.

Contribution

It introduces a novel approach that combines topological and variational techniques to find solutions without growth restrictions, considering the cone of nonnegative, nondecreasing radial functions.

Findings

Existence of positive increasing radial solutions established.

No growth restrictions on the nonlinearity at infinity.

Method handles lack of compactness via cone of functions.

Abstract

We study the existence of positive increasing radial solutions for superlinear Neumann problems in the ball. We do not impose any growth condition on the nonlinearity at infinity and our assumptions allow for interactions with the spectrum. In our approach we use both topological and variational arguments, and we overcome the lack of compactness by considering the cone of nonnegative, nondecreasing radial functions of H^1.