ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

doi:10.1007/s10473-022-0117-9

Abstract

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

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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