The cone Moser-Trudinger inequalities and applications

摘要

In this paper, we first study the cone Moser-Trudinger inequalities and their best exponents on both bounded and unbounded domains R-+(2). Then, using the cone Moser-Trudinger inequalities, we study the asymptotic behavior of Cerami sequences and the existence of weak solutions to the nonlinear equation{-Delta(B)u = f(x, u), in x is an element of int(B),u = 0, on partial derivative B,where Delta(B) is an elliptic operator with conical degeneration on the boundary x(1) = 0, and the nonlinear term f has the subcritical exponential growth or the critical exponential growth.