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Anisotropic (p, q)-equations with competition phenomena

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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.

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Authors and Affiliations

  1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, China

    Zhenhai Liu

  2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China

    Zhenhai Liu

  3. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

Authors
  1. Zhenhai Liu
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  2. Nikolaos S. Papageorgiou
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Correspondence to Zhenhai Liu.

Additional information

The work was supported by NNSF of China (12071413), NSF of Guangxi (2018GXNSFDA138002).

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Liu, Z., Papageorgiou, N.S. Anisotropic (p, q)-equations with competition phenomena. Acta Math Sci 42, 299–322 (2022). https://doi.org/10.1007/s10473-022-0117-9

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  • DOI: https://doi.org/10.1007/s10473-022-0117-9

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