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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 30 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1459343996

Digital Object Identifier
doi:10.12775/TMNA.2015.027

Mathematical Reviews number (MathSciNet)
MR3408836

Zentralblatt MATH identifier
1375.35126

Citation

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. https://projecteuclid.org/euclid.tmna/1459343996


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