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.

引用

页数：27

共 38 条

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[38] Multiple positive solutions for a fractional p&q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p \& q$$\end{document}-Laplacian system with concave and critical nonlinearities
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