Ground state solution for a class of differential equations with left and right fractional derivatives

Abstract

In this work we study the existence of solution for a class of fractional differential equation given by \begin{eqnarray}\label{eq00} _{t}D_{\infty}^α{_{-\infty}}D_{t}^αu(t) + u(t) = & f(t,u(t))\\ u\in H^α(\mathbb{R}).\nonumber \end{eqnarray} where $\alpha \in (1/2,1)$, $t\in \mathbb{R}$, $u\in \mathbb{R}$, $f\in C(\mathbb{R},\mathbb{R})$. Using mountain pass theorem and comparison argument we prove that (\ref{eq00}) at least has one nontrivial solution.

References in corpus (1)

• Fractional Hamiltonian analysis of higher order derivatives systems

Cited by in corpus (3)

• Multiplicity of solutions for fractional Hamiltonian systems with Liouville-Weyl fractional derivative
• Existence and multiplicity result for a fractional p-Laplacian equation with combined fractional derivatives
• Existence of solution for perturbed fractional Hamiltonian systems