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 Nonlinear Dirichlet problems with double resonance
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/17236

title: Nonlinear Dirichlet problems with double resonance
authors: Aizicovici, Sergiu
Papageorgiou, Nikolaos S.
Staicu, Vasile
keywords: p-Laplacian
Double resonance
Nonlinear regularity
Critical groups
Constant 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
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