带有临界指数增长的分数阶问题解的存在性

Existence of Solutions for a Fractional Laplacian Problem with Critical Exponential Growth

讨论了一类分数阶拟线性方程非平凡解的存在性,其非线性项与分数阶Trudinger-Moser型不等式有关,非线性项f(x,u)在无穷远处具有e^α|u|N N-s的临界指数增长,其中α>0,从而导致问题对应的能量泛函缺失紧性.

In this paper,we consider the existence of nontrivial solutions to a fractional quasilinear problem,whose nonlinear term is related to the fractional Trudinger-Moser-type inequality.The associated energy functional lacks compactness,because the nonlinear term f(x,u)is of critical exponential growth,which behaves like e^α|u|N N-s as u→+∞for someα>0.