Zero mass case for a fractional Berestycki-Lions type problem

Abstract

In this work we study the following fractional scalar field equation \begin{equation*}\label{P} \left\{ \begin{array}{ll} (-Δ)^{s} u = g'(u) \mbox{ in } \mathbb{R}^{N} \\ u> 0 \end{array} \right. \end{equation*} where $N\ge 2$, $s\in (0,1)$, $(-\Delta {)}^s$ is the fractional Laplacian and the nonlinearity $g\in C^2(\mathbb{R})$ is such that $g^{\prime \prime }(0)=0$. By using variational methods, we prove the existence of a positive solution which is spherically symmetric and decreasing in $r=|x|$.

References in corpus (3)

• Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
• Ground states solutions for a non-linear equation involving a pseudo-relativistic Schrödinger operator
• Existence of multiple solutions of $p$-fractional Laplace operator with sign-changing weight function

Cited by in corpus (3)

• Sign-changing solutions for a class of fractional Schrödinger equations with vanishing potentials
• Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions
• Degenerate fractional Kirchhoff-type system with magnetic fields and upper critical growth