arXiv subjects

Ricardo Lima Alves

Publications and source records attributed to Ricardo Lima Alves.

4 recordsLinked to original sources

arXiv2022

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

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 $λ>0$ 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.

math.AP↗

arXiv2020

A new result on the existence and non-existence of positive solutions for two-parametric systems of quasilinear elliptic equations

This paper is devoted to the existence and non-existence of positive solutions for a $(p, q)$-Laplacian system with indefinite nonlinearity depending on two parameters $(λ,μ)$. By using the sub-supersolution method together with adaptations of ideas found in \cite{AAS,CRMZ}, we extend some previous result.

math.AP↗

arXiv2019

Existence of positive solution for a singular elliptic problem with an asymptotically linear nonlinearity

In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison techniques, we show the existence, uniqueness, non-existence and regularity of the solutions. We also obtain a bifurcation-type result.

math.AP↗

arXiv2019

About existence and regularity of positive solutions for a Quasilinear Schrödinger equation with singular nonlinearity

This paper deals with the existence of positive solution for the singular quasilinear Schrödinger equation $-Δu -Δ(u^{2})u=h(x) u^{-γ} + f(x,u)~\mbox{in} ~ Ω,$ where $γ> 1$, $Ω\subset \mathbb{R}^{N}, (N\geq 3)$ is a bounded smooth domain, $0<h\in L^{1}(Ω)$, $f$ is a measurable function that can change signal and can be sublinear or has critical growth. Inspired by Sun \cite{Y} we derive a compatible condition on the couple $(h(x),γ)$, which is optimal for the existence of $H_{0}^{1}$-solution for this problem.

math.AP↗