A note on the existence and multiplicity of solutions for sublinear fractional problems

Abstract

Abstract In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following L K p u = λ f ( x , u ) in Ω , u = 0 in R N ∖ Ω , $$ \begin{aligned} &\mathcal{L}^{p}_{K}u=\lambda f(x,u)&&\text{in }\Omega, \\ &u=0&&\text{in }\mathbb{R}^{N}\setminus\Omega, \end{aligned} $$ where L K p $\mathcal{L}^{p}_{K} $ is a nonlocal operator with singular kernel, Ω is an open bounded smooth domain of R N $\mathbb{R}^{N}$ . Our purpose is to generalize the known results for fractional Laplacian equations to fractional p-Laplacian equations.

Keywords

• fractional p-Laplacian problem
• variational method
• multiple solutions