Uniform result for solutions of an equation with boundary singularity

TL;DR

This paper analyzes solutions to a boundary singularity problem with exponential nonlinearity, providing blow-up analysis and compactness criteria to understand solution behavior.

Contribution

It introduces a blow-up analysis and compactness conditions for solutions of equations with boundary singularities and exponential nonlinearities.

Findings

Established a blow-up analysis for solution sequences.

Derived a compactness criterion under specific conditions.

Enhanced understanding of solution behavior near boundary singularities.

Abstract

We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some conditions.