Repositório Institucional da Universidade de Aveiro > CIDMA - Centro de Investigação e Desenvolvimento em Matemática e Aplicações > CIDMA - Artigos > Nonlinear Dirichlet problems with double resonance
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 title: Nonlinear Dirichlet problems with double resonance authors: Aizicovici, SergiuPapageorgiou, Nikolaos S.Staicu, Vasile keywords: p-LaplacianDouble resonanceNonlinear regularityCritical groupsConstant sign and nodal solutions issue date: Jul-2017 publisher: American Institute of Mathematical Sciences (AIMS) abstract: We study a nonlinear Dirichlet problem driven by the sum of a $p-$Laplacian ($p>2$) and a Laplacian and which at $\pm\infty$ is resonant with respect to the spectrum of $\left( -\triangle_{p},W_{0}^{1,p}\left( \Omega\right) \right)$ and at zero is resonant with respect to the spectrum of $\left( -\triangle,H_{0}^{1}\left( \Omega\right) \right)$ (double resonance). We prove two multiplicity theorems providing three and four nontrivial solutions respectivelly, all with sign information. Our approach uses critical point theory together with truncation and comparison techniques and Morse theory. URI: http://hdl.handle.net/10773/17236 ISSN: 1534-0392 publisher version/DOI: http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=13910 source: Communications on Pure and Applied Analysis appears in collections CIDMA - Artigos

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