Existence and non-existence results for quasilinear elliptic exterior problems with nonlinear boundary conditions

TL;DR

This paper investigates conditions under which solutions exist or do not exist for quasilinear elliptic exterior problems with nonlinear boundary conditions, using variational methods and geometric analysis.

Contribution

It provides new existence and non-existence results for complex elliptic problems involving nonlinear boundary conditions and non-compactness, advancing theoretical understanding.

Findings

Established criteria for existence of solutions.

Identified conditions leading to non-existence.

Combined variational and geometric methods effectively.

Abstract

Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition between the different growths of the non-linearities.