A Multiplicity Theorem for Superlinear Double Phase Problems

A Multiplicity Theorem for Superlinear Double Phase Problems

We consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive...

Full description

Bibliographic Details
Main Authors: Beata Derȩgowska, Leszek Gasiński, Nikolaos S. Papageorgiou
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Symmetry
Subjects:
double phase operator
Nehari manifold
superlinear reaction
constant sign and nodal solutions
Musielak–Orlicz spaces
Online Access:https://www.mdpi.com/2073-8994/13/9/1556
Description
Summary:We consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive and by the symmetry of the behaviour at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mo>∞</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mo>∞</mo></mrow></semantics></math></inline-formula> also negative.
ISSN:2073-8994

Similar Items