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Marco A. S. Souto

Publications and source records attributed to Marco A. S. Souto.

11 recordsLinked to original sources
arXiv2018

Existence of solution for a nonlocal dispersal model with nonlocal term via bifurcation theory

In this paper we study the existence of solution for the following class of nonlocal problems \[ L_0u =u \left(λ- \int_ΩQ(x,y) |u(y)|^p dy \right) , \ \mbox{in} \ Ω, \] where $Ω\subset \mathbb{R}^{N}$, $N\geq 1$, is a bounded connected open, $p>0$, $λ$ is a real parameter, $Q:Ω\times Ω\to \mathbb{R}$ is a nonnegative function, and $L_0 : C(\overlineΩ) \to (\overlineΩ)$ is a nonlocal dispersal operator. The existence of solution is obtained via bifurcation theory.

math.AP↗
arXiv2017

A Berestycki-Lions type result and applications

In this paper we show an abstract theorem involving the existence of critical points for a functional $I$, which permit us to prove the existence of solutions for a large class of Berestycki-Lions type problems. In the proof of the abstract result we apply the deformation lemma on a special set associated with $I$, which we call of Pohozaev set.

math.AP↗
arXiv2016

Existence of positive solution for a system of elliptic equations via bifurcation theory

In this paper we study the existence of solution for the following class of system of elliptic equations $$ \left\{ \begin{array}{lcl} -Δu=\left(a-\int_ΩK(x,y)f(u,v)dy\right)u+bv,\quad \mbox{in} \quad Ω -Δv=\left(d-\int_ΩΓ(x,y)g(u,v)dy\right)v+cu,\quad \mbox{in} \quad Ωu=v=0,\quad \mbox{on} \quad \partialΩ \end{array} \right. \eqno{(P)} $$ where $Ω\subset\R^N$ is a smooth bounded domain, $N\geq1$, and $K,Γ:Ω\timesΩ\rightarrow\R$ is a nonnegative function checking some hypotheses and $a,b,c,d\in\R$. The functions $f$ and $g$ satisfy some conditions which permit to use Bifurcation Theory to prove the existence of solution for $(P)$.

math.AP↗
arXiv2015

Existence of solution for a nonlocal problem in $\R^N$ via bifurcation theory

In this paper, we study the existence of solution for the following class of nonlocal problem, $$ \left\{ \begin{array}{lcl} -Δu=\left(λf(x)-\int_{\R^N}K(x,y)|u(y)|^γdy\right)u,\quad \mbox{in} \quad \R^{N}, \\ \displaystyle \lim_{|x| \to +\infty}u(x)=0,\quad u>0 \quad \text{in} \quad \R^{N}, \end{array} \right. \eqno{(P)} $$ where $N\geq3$, $λ>0, γ\in[1,2)$, $f:\R\rightarrow\R$ is a positive continuous function and $K:\R^N\times\R^N\rightarrow\R$ is a nonnegative function. The functions $f$ and $K$ satisfy some conditions, which permit to use Bifurcation Theory to prove the existence of solution for problem $(P)$.

math.AP↗
arXiv2015

Choquard Equations with Mixed Potential

In this paper, we study the following class of nonlinear Choquard equation, $$-Δu+a(z)u=K(u)f(u)\quad \text{in}\quad \R^N,$$ where $\R^N=\R^L\times\R^M$, $L\geq2$, $K(u)=|.|^{-γ}*F(u)$, $γ\in(0,N)$, $a$ is a continuous real function and $F$ is the primitive function of $f$. Under some suitable assumptions mixed on the potential $a$. We prove existence of a nontrivial solution for the above equation.

math.AP↗
arXiv2014

A sign-changing solution for the Schrödinger-Poisson equation

We find a sign-changing solution for a class of Schrödinger-Poisson system in $\mathbb{R}^3$ as an existence result by minimization in a closed subset containing all the sign-changing solutions of the equation. The proof is based on variational methods in association with the deformation lemma and Miranda's theorem.

math.AP↗