Asymptotic behavior of positive solutions of a~Dirichlet problem involving supercritical nonlinearities

Commentationes mathematicae Universitatis Carolinae

Giovanni Anello¹ 

关键词: elliptic boundary value problems;    positive solutions;    variational methods;    asymptotic behavior;    combined nonlinearities;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

Let $p>1$, $q>p$, $\lambda >0$ and $s\in ]1,p[$. We study, for $s\rightarrow p^-$, the behavior of positive solutions of the problem $-\Delta_p u = \lambda u^{s-1}+u^{q-1}$ in $\Omega$, $u_{\mid\partial \Omega}=0$. In particular, we give a positive answer to an open question formulated in a recent paper of the first author.

【 授权许可】

CC BY