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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João R. Santos was partially supported by CNPq 306503/2018-7, Brazil. Gaetano Siciliano was partially supported by Fapesp 2019/27491-0, Capes and CNPq 304660/2018-3, Brazil.
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Gasiński, L., Santos Junior, J.R. & Siciliano, G. Positive solutions for a class of nonlocal problems with possibly singular nonlinearity. J. Fixed Point Theory Appl. 24, 65 (2022). https://doi.org/10.1007/s11784-022-00982-5
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DOI: https://doi.org/10.1007/s11784-022-00982-5