ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

doi:10.1007/s10473-022-0117-9

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 299-322.doi: 10.1007/s10473-022-0117-9

ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

刘振海^1,2, Nikolaos S. PAPAGEORGIOU³

1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, China;
2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China;
3. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

收稿日期:2020-06-15 修回日期:2021-06-09 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Zhenhai LIU,E-mail:zhhliu@hotmail.com E-mail:zhhliu@hotmail.com
作者简介:Nikolaos S. PAPAGEORGIOU,E-mail:npapg@math.ntua.gr
基金资助:
The work was supported by NNSF of China (12071413), NSF of Guangxi (2018GXNSFDA138002).

ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

Zhenhai LIU^1,2, Nikolaos S. PAPAGEORGIOU³

1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, China;
2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China;
3. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

Received:2020-06-15 Revised:2021-06-09 Online:2022-02-25 Published:2022-02-24
Contact: Zhenhai LIU,E-mail:zhhliu@hotmail.com E-mail:zhhliu@hotmail.com
Supported by:
The work was supported by NNSF of China (12071413), NSF of Guangxi (2018GXNSFDA138002).

摘要/Abstract

摘要： We consider a nonlinear Robin problem driven by the anisotropic (p, q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear (concave) term and of a superlinear (convex) term. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies. We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

关键词: concave-convex nonlinearities, anisotropic operators, regularity theory, maximum principle, minimal positive solution

Abstract: We consider a nonlinear Robin problem driven by the anisotropic (p, q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear (concave) term and of a superlinear (convex) term. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies. We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

Key words: concave-convex nonlinearities, anisotropic operators, regularity theory, maximum principle, minimal positive solution

中图分类号:

35J75

刘振海, Nikolaos S. PAPAGEORGIOU. ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA[J]. 数学物理学报(英文版), 2022, 42(1): 299-322.

Zhenhai LIU, Nikolaos S. PAPAGEORGIOU. ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA[J]. Acta mathematica scientia,Series B, 2022, 42(1): 299-322.

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ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

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