ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

doi:10.1007/s10473-022-0210-0

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 561-574.doi: 10.1007/s10473-022-0210-0

ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

Salvatore LEONARDI¹, Nikolaos S. PAPAGEORGIOU²

1. Dipartimento di Matematica e Informatica, Viale A. Doria, 6 95125 Catania, Italy;
2. Technical University, Department of Mathematics, Zorografou Campus, Athens 15780, Greece

收稿日期:2020-04-17 出版日期:2022-04-25 发布日期:2022-04-22
作者简介:Salvatore LEONARDI,E-mail:leonardi@dmi.unict.it;Nikolaos S. PAPAGEORGIOU,E-mail:npapg@math.ntua.gr
基金资助:
This work has been supported by Piano della Ricerca di Ateneo 2020-2022- PIACERI:Project MO.S.A.I.C. "Monitoraggio satellitare, modellazioni matematiche e soluzioni architettoniche e urbane per lo studio, la previsione e la mitigazione delle isole di calore urbano", Project EEEP&DLaD. S. Leonardi is member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

Salvatore LEONARDI¹, Nikolaos S. PAPAGEORGIOU²

1. Dipartimento di Matematica e Informatica, Viale A. Doria, 6 95125 Catania, Italy;
2. Technical University, Department of Mathematics, Zorografou Campus, Athens 15780, Greece

Received:2020-04-17 Online:2022-04-25 Published:2022-04-22
Supported by:
This work has been supported by Piano della Ricerca di Ateneo 2020-2022- PIACERI:Project MO.S.A.I.C. "Monitoraggio satellitare, modellazioni matematiche e soluzioni architettoniche e urbane per lo studio, la previsione e la mitigazione delle isole di calore urbano", Project EEEP&DLaD. S. Leonardi is member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

摘要/Abstract

摘要： We consider a nonlinear Robin problem driven by the $(p,q)$-Laplacian plus an indefinite potential term and with a parametric reaction term. Under minimal conditions on the reaction function, which concern only its behavior near zero, we show that, for all $\lambda >0$ small, the problem has a nodal solution $y_{\lambda} \in C^1(\bar{Ω})$ and we have $y_{\lambda} \rightarrow 0$ in $C^1(\bar{Ω})$ as $\lambda \rightarrow 0^+$.

关键词: (p, q)-Laplacian, indefinite potential, nonlinear regularity, extremal constant sign solutions, nodal solutions

Abstract: We consider a nonlinear Robin problem driven by the $(p,q)$-Laplacian plus an indefinite potential term and with a parametric reaction term. Under minimal conditions on the reaction function, which concern only its behavior near zero, we show that, for all $\lambda >0$ small, the problem has a nodal solution $y_{\lambda} \in C^1(\bar{Ω})$ and we have $y_{\lambda} \rightarrow 0$ in $C^1(\bar{Ω})$ as $\lambda \rightarrow 0^+$.

Key words: (p, q)-Laplacian, indefinite potential, nonlinear regularity, extremal constant sign solutions, nodal solutions

中图分类号:

35J20

Salvatore LEONARDI, Nikolaos S. PAPAGEORGIOU. ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL[J]. 数学物理学报(英文版), 2022, 42(2): 561-574.

Salvatore LEONARDI, Nikolaos S. PAPAGEORGIOU. ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL[J]. Acta mathematica scientia,Series B, 2022, 42(2): 561-574.

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ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

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