Abstract
In this paper we consider the following nonlinear elliptic problem: $-\Delta u=Ku^3,$ $u>0$ in $\Omega$, $u=0$ on $\partial\Omega$, where $K$ is a positive function and $\Omega$ is a bounded domain of $R^4$. We prove a version of the Morse lemma at infinity for this problem, which allows us to describe the critical points at infinity of the associated variational problem. Using a topological argument, we are able to prove an existence result.
Citation
Mokhless Hammami. Mohamed ben Ayed. "On a variational problem involving critical Sobolev growth in dimension four." Adv. Differential Equations 9 (3-4) 415 - 446, 2004. https://doi.org/10.57262/ade/1355867950
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