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

2013/08/20 by César Torres, Torres, César · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1308.4215

arxiv created 2013/08/20 · openalex publication_date 2013/08/20 · arxiv updated 2013/08/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this work we study the existence of solution for a class of fractional differential equation given by _tD_∞^α_-∞D_t^αu(t) + u(t) = f(t,u(t))
u∈ H^α(ℝ).where α∈ (1/2, 1), t∈ ℝ, u∈ ℝ, f∈ C(ℝ, ℝ). Using mountain pass theorem and comparison argument we prove that (\refeq00) at least has one nontrivial solution.

Citations

• Fractional Differential Equations

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• Existence and symmetric result for Liouville-Weyl fractional nonlinear Schrödinger equation

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