ANISOTROPIC(p,q)-EQUATIONS WITH COMPETITION PHENOMENA  

作　　者：Zhenhai LIU Nikolaos S.PAPAGEORGIOU 刘振海;Nikolaos S.PAPAGEORGIOU(Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,Yulin Normal University,Yulin 537000,China;Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis,Guangxi University for Nationalities,Nanning 530006,China;Department of Mathematics,National Technical University,Zografou Campus,15780 Athens.Greece)

机构地区：[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 530006,China [3]Department of Mathematics,National Technical University,Zografou Campus,15780 Athens.Greece

出　　处：《Acta Mathematica Scientia》2022年第1期299-322,共24页数学物理学报（B辑英文版）

基　　金：supported by NNSF of China(12071413);NSF of Guangxi(2018GXNSFDA138002)。

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 

分 类 号：O175[理学—数学]