The cone Moser–Trudinger inequalities and applications

Article type: Research Article

Authors: Fang, Fei^a | Ji, Chao^{b; *}

Affiliations: [a] Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China | [b] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: 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.

Keywords: Cone Moser–Trudinger inequalities, best exponent, asymptotic estimate, rearrangement, mountain pass theorem

DOI: 10.3233/ASY-191588

Journal: Asymptotic Analysis, vol. 120, no. 3-4, pp. 273-299, 2020