Multiple solutions for nonlinear boundary value problems of Kirchhoff type on a double phase setting

TL;DR

This paper establishes multiple solutions for nonlinear Kirchhoff boundary value problems on a double phase setting, using variational, truncation, and topological methods under broad assumptions.

Contribution

It introduces new multiplicity results for Kirchhoff problems with nonlinear boundary conditions without relying on the Ambrosetti-Rabinowitz condition.

Findings

Multiple solutions are proven to exist under general conditions.

Results apply even when perturbations do not satisfy the Ambrosetti-Rabinowitz condition.

The approach combines variational, truncation, and topological techniques.

Abstract

This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations exhibit a suitable behavior in the origin and at infinity, or when they do not necessarily satisfy the Ambrosetti-Rabinowitz condition. To this aim, we combine variational methods, truncation arguments and topological tools.