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 −ΔBu=f(x,u),in x∈int(B),u=0,on ∂B, where ΔB is an elliptic operator with conical degeneration on the boundary x1=0, and the nonlinear term f has the subcritical exponential growth or the critical exponential growth.

中文翻译：

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锥Moser–Trudinger不等式及其应用

在本文中，我们首先研究有界和无界域R + 2上的锥Moser-Trudinger不等式及其最佳指数。然后，使用锥Moser-Trudinger不等式，研究Cerami序列的渐近行为和非线性方程−ΔBu = f（x，u），x∈int（B），u = 0，的弱解的存在，在∂B上，其中ΔB是在边界x1 = 0处具有圆锥退化的椭圆算子，而非线性项f具有次临界指数增长或临界指数增长。