Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (1): 299-322.doi: 10.1007/s10473-022-0117-9

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ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

Zhenhai LIU1,2, Nikolaos S. PAPAGEORGIOU3   

  1. 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).

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

CLC Number: 

  • 35J75
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