arXiv subjects

Denilson S. Pereira

Publications and source records attributed to Denilson S. Pereira.

3 recordsLinked to original sources

arXiv2016

Existence of multi-bump solutions to biharmonic operator with critical exponential growth in $\mathbb{R}^4$

Using variational methods, we establish existence of multi-bump solutions for the following class of problems $$ \left\{ \begin{array}{l} Δ^2 u +(λV(x)+1)u = f(u), \quad \mbox{in} \quad \mathbb{R}^{4}, u \in H^{2}(\mathbb{R}^{4}), \end{array} \right. $$ where $Δ^2$ is the biharmonic operator, $f$ is a continuous function with critical exponential growth and $V : \mathbb{R}^4 \rightarrow \mathbb{R}$ is a continuous function verifying some conditions.

math.AP↗

arXiv2014

Multiplicity of multi-bump type nodal solutions for a class of elliptic problems with exponential critical growth in $\mathbb{R}^2$

In this paper, we establish the existence and multiplicity of multi-bump nodal solutions for the following class of problems $$ -Δu+(λV(x)+1)u=f(u),~~\mbox{in}~~\mathbb{R}^2, $$ where $λ\in(0,\infty)$, $f$ is a continuous function with exponential critical growth and $V:\mathbb{R}^2\to \mathbb{R}$ is a continuous function verifying some hypotheses.

math.AP↗

arXiv2014

Existence and nonexistence of least energy nodal solution for a class of elliptic problem in $\mathbb{R}^{2}$

In this work, we prove the existence of least energy nodal solution for a class of elliptic problem in both cases, bounded and unbounded domain, when the nonlinearity has exponential critical growth in $\mathbb{R}^2$. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole $\mathbb{R}^{2}$.

math.AP↗