4.5 Article

Positive Solutions for Anisotropic Singular Dirichlet Problems

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Publisher

SPRINGERNATURE
DOI: 10.1007/s40840-022-01249-5

Keywords

Regularity theory; Maximum principle; Truncation; Positive solution; Minimal solution; Hardy's inequality

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The above study proves a bifurcation-type result on the Dirichlet problem, describing the changes in the set of positive solutions as the parameter varies.
We consider a Dirichlet problem driven by a (p(z), q(z))-Laplacian and a reaction involving the sum of a parametric singular term plus a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter lambda > 0 varies. Also we show that for every admissible parameter the problem has a smallest positive solution and obtain the monotonicity and continuity properties of the minimal solution map.

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