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We deal with nonlinear elliptic Dirichlet problems of the form
where is a bounded domain in , , and has supercritical growth from the viewpoint of Sobolev embedding. Our aim is to show that there exist bounded contractible non star-shaped domains , arbitrarily close to domains with nontrivial topology, such that the problem does not have nontrivial solutions. For example, we prove that if , , with and with and , then for all there exists such that the problem has only the trivial solution for all and .
Cite this article
Riccardo Molle, Donato Passaseo, Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 1, pp. 121–130DOI 10.4171/RLM/882