Article citationsMore>>

Xiang, M., Yang, D. and Zhang, B. (2020) Homoclinic Solutions for Hamiltonian Systems with Variable-Order Fractional Derivatives. Complex Variables and Elliptic Equations, 65, 1412-1432.
https://doi.org/10.1080/17476933.2019.1652281

has been cited by the following article:

• TITLE: Multiple Solutions for a Class of Variable-Order Fractional Laplacian Equations with Concave-Convex Nonlinearity

  AUTHORS: Canlin Gan, Ting Xiao, Qiongfen Zhang

  KEYWORDS: Concave-Convex Nonlinearity, Variable-Order Fractional Laplacian, Variational Methods, Fractional Elliptic Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.3, March 22, 2022

  ABSTRACT: This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in RN, s(⋅) ∈ C (RN × RN, (0,1)), (-Δ)s(⋅) is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.