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arXiv · 2006.13674

Positive solutions for a class of nonlocal problems with possibly singular nonlinearity

Leszek Gasiński·João R. Santos Junior·Gaetano Siciliano
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Abstract

We study a class of elliptic problems with homogeneous Dirichlet boundary condition and a nonlinear reaction term $f$ which is nonlocal depending on the $L^{p}$-norm of the unknown function. The nonlinearity $f$ can make the problem degenerate since it may even have multiple singularities in the nonlocal variable. We use fixed point arguments for an appropriately defined solution map to produce multiplicity of classical positive solutions with ordered norms.

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Leszek Gasiński, João R. Santos Junior, Gaetano Siciliano. 2020-06-24. Positive solutions for a class of nonlocal problems with possibly singular nonlinearity. https://arxiv.org/abs/2006.13674

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