Normalized solutions for a Schrodinger equation with critical growth in R-N

Author(s)

Alves, Claudianor O. ^[1] ; Ji, Chao ^[2] ; Miyagaki, Olimpio H. ^[3]

Affiliation

^[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429900 Campina Grande, Paraiba - Brazil

^[2] East China Univ Sci & Technol, Sch Math, Shanghai 200237 - Peoples R China

^[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 61, n. 1 FEB 2022.
• Web of Science Citations: 0

Abstract

In this paper we study the existence of normalized solutions to the following nonlinear Schrodinger equation with critical growth [-Delta u = lambda u + f(u), in R-N, u > 0, integral(RN) vertical bar u vertical bar(2) dx = a(2), where a > 0, lambda is an element of R and f has an exponential critical growth when N = 2, and f (t) = mu vertical bar t vertical bar(q-2)t + vertical bar t vertical bar(2{*}-2)t with q is an element of(2 + 4/N, 2{*}), mu > 0 and 2{*} = 2N/N-2 when N >= 3. Our main results complement some recent results for N >= 3 and it is totally new for N = 2. (AU)

• FAPESP's process: 19/24901-3 - Critical nonlocal quasilinear problem: existence, multiplicity and properties of the solutions
• Grantee: Olimpio Hiroshi Miyagaki
• Support Opportunities: Regular Research Grants