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.