Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain

Calogero Vetro, Mohamed Jleli, Bessem Samet, Awatif Alqahtani

Risultato della ricerca: Articlepeer review

Abstract

We study the large-time behavior of solutions to the nonlinear exterior problem Lu(t, x) = κ[pipe]u(t, x)[pipe]p, (t, x) ∈ (0, ∞) x Dc under the nonhomegeneous Neumann boundary condition (t, x) = λ(x), (t, x) ∈ (0, ∞) x ∂D, where L:= i∂t + Δ is the Schrodinger operator, D = B(0, 1) is the open unit ball in RN, N ≥ 2, Dc = RND, p > 1, κ ∈ , κ ≠ 0, λ ∈ L1(∂D, ) is a nontrivial complex valued function, and ∂v is the outward unit normal vector on ∂D, relative to Dc. Namely, under a certain condition imposed on (κ, λ), we show that if N ≥ 3 and p < pc, where pc =, then the considered problem admits no global weak solutions. However, if N = 2, then for all p > 1, the problem admits no global weak solutions. The proof is based on the test function method introduced by Mitidieri and Pohozaev, and an adequate choice of the test function.
Lingua originaleEnglish
pagine (da-a)1-9
Numero di pagine9
RivistaSymmetry
Volume12
Stato di pubblicazionePublished - 2020

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • ???subjectarea.asjc.2600.2600???
  • Physics and Astronomy (miscellaneous)

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