New Existence of Solutions for the Fractional p-Laplacian Equations with Sign-Changing Potential and Nonlinearity

Abstract

In the present paper, we consider the fractional p-Laplacian equation $$(-\Delta)_{p}^{s}u + V(x)|u|^{p-2}u = f(x, u),\quad \forall \in R^{N},$$ (1.1) where \({p \geq 2, N \geq 2}\), \({0 < s < 1}\), \({V \in C(R^N, R)}\) and \({f \in C(R^N \times R, R)}\) are allowed to be sign-changing. In such a double sign-changing case, a new result on the existence of nontrivial solutions for Eq. (1.1) is obtained via variational methods, which is even new for p = 2.