Critical Concave Convex Ambrosetti–Prodi Type Problems for Fractional 𝑝-Laplacian

Abstract

In this paper, we consider a class of critical concave convex Ambrosetti–Prodi type problems involving the fractional p-Laplacian operator. By applying the linking theorem and the mountain pass theorem as well, the interaction of the nonlinearities with the first eigenvalue of the fractional p-Laplacian will be used to prove existence of multiple solutions.

Keywords

• variational methods
• fractional equations
• nonlinear elliptic equations
• quasilinear equations
• critical exponents
• 35a15
• 35r11
• 35j60
• 35j62
• 35b33