A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems
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AuthorLópez Martínez, Salvador
Walter de Gruyter GmbH
López Martínez, S. (2019). A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems. arXiv preprint arXiv:1903.07894.
SponsorshipResearch supported by MINECO-FEDER grant MTM2015-68210-P, Junta de Andalucía FQM-116 and Programa de Contratos Predoctorales del Plan Propio de la Universidad de Granada.
We study a boundary value elliptic problem having a lower order nonlinear term with subquadratic growth in the gradient of the solution and possibly singular when the solution vanishes. If the singularity is mild enough (and even in the absence of the singularity), we prove an existence and multiplicity result. On the contrary, we prove an existence and uniqueness result for strong singularities.