Normalized solutions for an horizontal transmission problem

Author(s)

Figueiredo, Giovany M. ^[1] ; Siciliano, Gaetano ^[2]

Affiliation

^[1] Univ Brasilia, Dept Matemat, Brasilia, DF - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Sao Paulo - Brazil

• Document type: Journal article
• Source: APPLICABLE ANALYSIS; v. 100, n. 15, p. 3174-3181, NOV 18 2021.
• Web of Science Citations: 0

Abstract

Let Omega be a bounded and smooth domain in RN, N = 3. We study in this paper the following nonlinear transmission problem - u +.u = |u|p-2u in Omega, v + mu v = a(x)|v|q-2v in RN \textbackslash{} Omega, u = v and. u.n =.v. n = 0 on. Omega, where the unknowns are u : . R, v : RN \textbackslash{} . R and the real numbers., mu. Actually we are looking for solutions u, v with prescribed L2-norm. The problem has a variational formulation and indeed, under minimal assumptions, we are able to find infinitely many solutions by using the Krasnoselkii genus, whatever the L2-norm of u and v a priori is. (AU)

• FAPESP's process: 18/17264-4 - Existence of solutions for nonlinear elliptic equations
• Grantee: Gaetano Siciliano
• Support Opportunities: Regular Research Grants