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On Noncoercive (p, q)-Equations

Authors
  • Papageorgiou, Nikolaos S.1
  • Vetro, Calogero2
  • Vetro, Francesca3
  • 1 National Technical University, Zografou Campus, Athens, 15780, Greece , Athens (Greece)
  • 2 University of Palermo, Via Archirafi 34, Palermo, 90123, Italy , Palermo (Italy)
  • 3 3 , Palermo (Italy)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 29, 2021
Volume
41
Issue
5
Pages
1788–1808
Identifiers
DOI: 10.1007/s10473-021-0524-3
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

Abstract

We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p − 1)-linear near ±∞ and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

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