arXiv subjects

Edcarlos D. da Silva

Publications and source records attributed to Edcarlos D. da Silva.

4 recordsLinked to original sources

arXiv2017

Existence of solutions for critical Choquard equations via the concentration compactness method

In this paper we consider the nonlinear Choquard equation $$ -Δu+V(x)u =\left(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^μ}dy\right)g(x,u)\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N, $$ where $0<μ<N$, $N\geq3$, $g(x,u)$ is of critical growth due to the Hardy--Littlewood--Sobolev inequality and $G(x,u)=\displaystyle\int^u_0g(x,s)ds$. Firstly, by assuming that the potential $V(x)$ might be sign-changing, we study the existence of Mountain-Pass solution via a concentration-compactness principle for the Choquard equation. Secondly, under the conditions introduced by Benci and Cerami \cite{BC1}, we also study the existence of high energy solution by using a global compactness lemma for the nonlocal Choquard equation.

math.AP↗

arXiv2017

Multiplicity of Solutions for Quasilinear Elliptic Problems

It is established existence, uniqueness and multiplicity of solutions for a quasilinear elliptic problem problems driven by $Φ$-Laplacian operator. Here we consider the reflexive and nonreflexive cases using an auxiliary problem. In order to prove our main results we employ variational methods, regularity results and truncation techniques.

math.AP↗

arXiv2012

Multiplicity of solutions for gradient systems under strong resonance at the first eigenvalue

In this paper we establish existence and multiplicity of solutions for an elliptic system which has strong resonance at first eigenvalue. To describe the resonance, we use an eigenvalue problem with indefinite weight. In all results we use Variational Methods.

math.AP↗

arXiv2012

Ressonant elliptic problems under Cerami condition

We establish existence and multiplicity of solutions for a elliptic resonant elliptic problem under Dirichlet boundary conditions.

math.AP↗