Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations

We consider a nonlinear Dirichlet equation driven by the sum of a p -Laplacian and of a Laplacian (a ( p , 2)-equation). The hypotheses on the reaction f ( z ,  x ) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2020-05, Vol.43 (3), p.2343-2371
Main Authors: Papageorgiou, Nikolaos S., Vetro, Calogero, Vetro, Francesca
Format: Article
Language:English
Subjects:
Applications of Mathematics
Coercivity
Dirichlet problem
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
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Summary:We consider a nonlinear Dirichlet equation driven by the sum of a p -Laplacian and of a Laplacian (a ( p , 2)-equation). The hypotheses on the reaction f ( z ,  x ) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric ( p , 2)-equations.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-019-00808-7