ON NONCOERCIVE (p,q)-EQUATIONS

doi:10.1007/s10473-021-0524-3

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1788-1808.doi: 10.1007/s10473-021-0524-3

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

收稿日期:2020-03-31 修回日期:2021-04-10 出版日期:2021-10-25 发布日期:2021-10-21
通讯作者: Francesca VETRO E-mail:francescavetro80@gmail.com
作者简介:Nikolaos S. PAPAGEORGIOU,E-mail:npapg@math.ntua.gr;Calogero VETRO,E-mail:calogero.vetro@unipa.it

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

摘要/Abstract

摘要： 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.

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

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

中图分类号:

35J20

Nikolaos S. PAPAGEORGIOU, Nikolaos S. PAPAGEORGIOU, Calogero VETRO. ON NONCOERCIVE (p,q)-EQUATIONS[J]. 数学物理学报(英文版), 2021, 41(5): 1788-1808.

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

ON NONCOERCIVE (p,q)-EQUATIONS

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