Year: 2024
Author: Jian-Wen Sun
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 4 : pp. 1022–1030
Abstract
In this paper, we study the positive solutions of the semilinear elliptic equation $$\begin{cases} Lu+g(x,u)u=0 \ \ &{\rm in}& \Omega, \\ Bu=0 \ \ &{\rm on}& ∂Ω, \end{cases}$$where $\Omega ⊂\mathbb{R}^N$ is a bounded smooth domain, $L$ is an elliptic operator, $B$ is a general boundary operator and $g(·, ·)$ is a continuous function. This is a general problem proposed by Amann [Arch. Rational Mech. Anal. 44 (1972)], Cac [J. London Math. Soc. 25 (1982)] and Hess [Math. Z. 154 (1977)]. We obtain various uniqueness results when the nonlinearity function $g$ satisfies some additional conditions.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.1022
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 4 : pp. 1022–1030
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Elliptic reaction-diffusion equation uniqueness.