On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations

TL;DR

This paper investigates the uniqueness and existence of boundary blow-up solutions for certain nonlinear elliptic equations involving second order elliptic operators with measurable coefficients.

Contribution

It provides new uniqueness theorems and an existence theorem for boundary blow-up solutions of semilinear elliptic equations with specific nonlinearities.

Findings

Established uniqueness theorems for boundary blow-up solutions.

Proved an existence theorem for solutions under certain conditions.

Analyzed equations with nonlinearities like $u_+^p$ and $e^{au}$.

Abstract

We study boundary blow-up solutions of semilinear elliptic equations $Lu=u_+^p$ with $p>1$, or $Lu=e^{au}$ with $a>0$, where $L$ is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.