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arXiv · 2109.10289

Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems

Ricardo Lima Alves
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Abstract

In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter $\lambda>0$ varies. In our first result, the superlinear perturbation has an arbitrary growth and we obtain the existence of a solution for the problem by using the sub-supersolution method. For the second result, the superlinear perturbation has subcritical growth and we employ the Mountain Pass Theorem to show the existence of a second solution.

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Ricardo Lima Alves. 2021-09-21. Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems. https://arxiv.org/abs/2109.10289

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