The Multiplicity of Solutions for a Certain Class of Fractional Elliptic Equation

摘要

This paper explores the multiplicity of solutions for a Certain class of fractional elliptic equation under the Dirichlet boundary conditions. By using the asymptotic property of the nonlinear term f(x, u) at zero and at infinite point, the mountain pass theorem and proper truncation methods can be applied to get both a positive and a negative solution for all parameters under the condition of not satisfying the Ambrosetti-Rabinowitz.