Radial positive solutions for mixed local and nonlocal supercritical Neumann problem

TL;DR

This paper proves the existence of positive radial solutions for a nonlinear mixed local and nonlocal Neumann problem in a ball, without growth restrictions on the nonlinearity, and offers criteria for non-constant solutions.

Contribution

It introduces new existence results for positive radial solutions in a mixed local and nonlocal supercritical Neumann problem without growth assumptions.

Findings

Existence of positive non-decreasing radial solutions.

Criteria for the existence of non-constant solutions.

No growth condition required on the nonlinearity.

Abstract

In this paper, we establish the existence of positive non-decreasing radial solutions for a nonlinear mixed local and nonlocal Neumann problem in the ball. No growth assumption on the nonlinearity is required. We also provide a criterion for the existence of non-constant solutions provided the problem possesses a trivial constant solution.