ON NONCOERCIVE (p,q)-EQUATIONS

doi:10.1007/s10473-021-0524-3

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (5): 1788-1808.doi: 10.1007/s10473-021-0524-3

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ON NONCOERCIVE (p,q)-EQUATIONS

Nikolaos S. PAPAGEORGIOU¹, Nikolaos S. PAPAGEORGIOU², Calogero VETRO³

1. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece;
2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy;
3. 90123, Palermo, Italy

Received:2020-03-31 Revised:2021-04-10 Online:2021-10-25 Published:2021-10-21
Contact: Francesca VETRO E-mail:francescavetro80@gmail.com

Abstract

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.

Key words: (p,q)-Laplacian, principal eigenvalue, constant sign and nodal solutions, extremal solutions, nonlinear regularity

CLC Number:

35J20

Nikolaos S. PAPAGEORGIOU, Nikolaos S. PAPAGEORGIOU, Calogero VETRO. ON NONCOERCIVE (p,q)-EQUATIONS[J].Acta mathematica scientia,Series B, 2021, 41(5): 1788-1808.

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ON NONCOERCIVE (p,q)-EQUATIONS

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