A Landesman–Lazer Local Condition for Semilinear Elliptic Problems

2019 ◽  
Vol 50 (4) ◽  
pp. 889-911 ◽  
Author(s):  
M. C. M. Rezende ◽  
P. M. Sánchez-Aguilar ◽  
E. A. B. Silva
Keyword(s):  
Elliptic Problems ◽  
Local Condition ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems

Asymptotic behaviour of positive solutions of semilinear elliptic problems with increasing powers

2021 ◽  
pp. 1-18
Author(s):  
Lucio Boccardo ◽  
Liliane Maia ◽  
Benedetta Pellacci
Keyword(s):  
Linear Operator ◽  
Asymptotic Behaviour ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Existence Results ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Image Position

We prove existence results of two solutions of the problem \[ \begin{cases} L(u)+u^{m-1}=\lambda u^{p-1} & \text{in}\ \Omega,\\ u>0 & \text{in}\ \Omega,\\ u=0 & \text{on}\ \partial \Omega, \end{cases} \] where $L(v)=-\textrm {div}(M(x)\nabla v)$ is a linear operator, $p\in (2,2^{*}]$ and $\lambda$ and $m$ sufficiently large. Then their asymptotical limit as $m\to +\infty$ is investigated showing different behaviours.

Sign in / Sign up

Export Citation Format

Share Document