Fractional p-Laplacian Equations with Subcritical and Critical Exponential Growth Without the Ambrosetti-Rabinowitz Condition

摘要

The main purpose of this paper is to investigate the existence of nontrivial solutions to a class of quasilinear non-local problems which do not satisfy the Ambrosetti-Rabinowitz (AR) condition where the nonlinear terms are superlinear at 0 and of subcritical or critical exponential growth (subcritical polynomial growth) at infinity. Some existence results for nontrivial solution are obtained using mountain pass theorem combined with the fractional Moser-Trudinger inequality.