Multiple solutions for Robin (p, q)-equations plus an indefinite potential and a reaction concave near the origin

被引：3
作者：
Papageorgiou, Nikolaos S. [1 ]
Scapellato, Andrea [2 ]
机构：
[1] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece
[2] Univ Catania, Dipartimento Matemat & Informat, Viale Andrea Doria 6, I-95125 Catania, Italy
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2021年 / 11卷 / 02期
关键词：
(p; q)-Laplacian; Indefinite potential; Resonant and superlinear reaction; Nonlinear regularity; Nonlinear maximum principle; Nodal solutions; Locally concave term; 35J20; 35J60;
D O I：
10.1007/s13324-021-00482-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a Robin problem driven by the (p, q)-Laplacian plus an indefinite potential term. The reaction is either resonant with respect to the principal eigenvalue or (p-1)-superlinear but without satisfying the Ambrosetti-Rabinowitz condition. For both cases we show that the problem has at least five nontrivial smooth solutions ordered and with sign information. When q=2 (a (p, 2)-equation), we show that we can slightly improve the conclusions of the two multiplicity theorems.
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页数：27
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