Topological Methods in Nonlinear Analysis

Solutions with sign information for nonlinear nonhomogeneous elliptic equations

Nikolaos S. Papageorgiou and Vicenţiu D. Rădulescu

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We consider a class of nonlinear, coercive elliptic equations driven by a nonhomogeneous differential operator. Using variational methods together with truncation and comparison techniques, we show that the problem has at least three nontrivial solutions, all with sign information. In the special case of $(p,2)$-equations, using tools from Morse theory, we show the existence of four nontrivial solutions, all with sign information. Finally, for a special class of parametric equations, we obtain multiplicity theorems that substantially extend earlier results on the subject.

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Topol. Methods Nonlinear Anal., Volume 45, Number 2 (2015), 575-600.

First available in Project Euclid: 30 March 2016

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Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D. Solutions with sign information for nonlinear nonhomogeneous elliptic equations. Topol. Methods Nonlinear Anal. 45 (2015), no. 2, 575--600. doi:10.12775/TMNA.2015.027.

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