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- W2912652978 abstract "We deals with nonlinear elliptic Dirichlet problems of the form $${rm div}(|D u|^{p-2}D u )+f(u)=0quadmbox{ in }Omega,qquad uin H^{1,p}_0(Omega) $$ where $Omega$ is a bounded domain in $mathbb{R}^n$, $nge 2$, $p> 1$ and $f$ has supercritical growth from the viewpoint of Sobolev embedding. Our aim is to show that there exist bounded contractible non star-shaped domains $Omega$, arbitrarily close to domains with nontrivial topology, such that the problem does not have nontrivial solutions. For example, we prove that if $n=2$, $1 {2pover 2-p}$ and $Omega={(rhocostheta,rhosintheta) : |theta| {2pover 2-p}$ there exists $bar s>0$ such that the problem has only the trivial solution $uequiv 0$ for all $alphain (0,pi)$ and $sin (0,bar s)$." @default.
- W2912652978 created "2019-02-21" @default.
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- W2912652978 date "2019-02-06" @default.
- W2912652978 modified "2023-09-27" @default.
- W2912652978 title "Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains" @default.
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