TY - JOUR
T1 - Uniqueness for the Semilinear Elliptic Problems
AU - Sun , Jian-Wen
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1022
EP - 1030
PY - 2024
DA - 2024/12
SN - 6
DO - http://doi.org/10.12150/jnma.2024.1022
UR - https://global-sci.org/intro/article_detail/jnma/23669.html
KW - Elliptic, reaction-diffusion equation, uniqueness.
AB - <p style="text-align: justify;">In this paper, we study the positive solutions of the semilinear
elliptic equation $$\begin{cases} Lu+g(x,u)u=0 \ \ &amp;{\rm in}&amp; \Omega, \\ Bu=0 \ \ &amp;{\rm on}&amp; ∂Ω,&nbsp;\end{cases}$$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.</p>