arXiv subjects

Rodrigo de Freitas Gabert

Publications and source records attributed to Rodrigo de Freitas Gabert.

2 recordsLinked to original sources

arXiv2018

Signed and sign-changing solutions for a class Kirchhoff-type problem involving the fractional p-Laplacian with critical Hardy nonlinearity

In this paper, we study the existence of three solutions for a Kirchhoff equation involving the nonlocal fractional p-Laplacian considering Sobolev and Hardy nonlinearities at subcritical and critical growths. The proof is based on Mountain Pass Theorem, Ekeland's variational principle and constrained minimization in Nehari sets.

math.AP↗

arXiv2018

Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities

We study the existence of least energy sign-changing solution for the fractional equation $(-Δ)^{s} u=|u|^{2_{s}^{*}-2}u+λf(x,u)$ in a smooth bounded domain $Ω$ of $\mathbb{R}^{N},$ $u=0$ in $\mathbb{R}^{N}\setminus Ω$, where $s\in (0,1)$ and $2_{s}^{*}$ is the fractional critical Sobolev exponent. The proof is based on constrained minimization in a subset of Nehari manifold, containing all the possible sign-changing solutions of the equation.

math.AP↗