Concentration phenomenon in the critical exponent problems on hyperbolic space. Issue 15 (18th November 2021)

• Record Type: Journal Article
• Authors: Mukherjee, Tuhina
• Is Part Of: Applicable analysis. Volume 100:Issue 15(2021)
• Page Start: 3117
• Page End: 3131
• Publication Date: 2021-11-18
• Subjects: Critical exponent problems -- hyperbolic space -- Nehari manifold -- least energy solutions; 35R11 -- 35R09 -- 35A15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1712367
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This article deals with the study of the following critical exponent problem 1 ( P λ, μ ) − Δ H n u + ( μ g ( x ) − λ ) u = u p − 1 i n H n, u > 0 i n H n, u ∈ H 1 ( H n ) where H n is the n -dimensional hyperbolic space, n ≥ 4, p = 2 n / ( n − 2 ) is the critical exponent, λ, μ > 0 are real parameters, Δ H n denotes the Laplace–Beltrami operator on H n and g ( x ) is a real valued potential function on H n . Using variational methods, we establish the existence of positive ground state solution to ( P λ, μ ) and study the convergence of these solutions when μ approaches + ∞ .