Ricardo Lima Alves
Published 2021-09-21Version 1
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.
A topological approach to the existence and multiplicity of positive solutions of $(p,q)$-Laplacian systems
Existence and multiplicity of positive solutions for the fractional Laplacian under subcritical or critical growth
On multiplicity of eigenvalues and symmetry of eigenfunctions of the $p$-Laplacian
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