Citas bibligráficas
Cuti, H., (2023). Existencia de solución débil para un problema asintóticamente periódico de la ecuación de Schrödinger no lineal con laplaciano fraccionario regional [Universidad Nacional de Trujillo]. https://hdl.handle.net/20.500.14414/18955
Cuti, H., Existencia de solución débil para un problema asintóticamente periódico de la ecuación de Schrödinger no lineal con laplaciano fraccionario regional []. PE: Universidad Nacional de Trujillo; 2023. https://hdl.handle.net/20.500.14414/18955
@phdthesis{renati/1049481,
title = "Existencia de solución débil para un problema asintóticamente periódico de la ecuación de Schrödinger no lineal con laplaciano fraccionario regional",
author = "Cuti Gutiérrez, Hernán Arquímides",
publisher = "Universidad Nacional de Trujillo",
year = "2023"
}
In this work, we study the nonlinear Scho¨dinger equation with nonlocal regional diffusion (P ) (−Δ)su + V (x)u = f (x, u) in RN , u ∈ Xs(RN ) , where s ∈ (0, 1), N ≥ 2, V : RN → R and f : RN × R → R are continuous functions and the operador (−Δ)s is a variational version of the nonlocal regional Laplacian defined as ∫RN ( Δ)su(x)v(x) dx = RN ∫B(0,ρ(x)) [u(x + z) − u(x)][v(x + z) − v(x)] dzdx , |z|N +2s where ρ C(RN, R+), when ρ, V and f ( , t) are periodic or asymptotically periodic at in- finity. The existence of minimum energy solutions of this problem is obtained by means of a comparison method, which consists in comparing the energy levels of the periodic case and the non-periodic case (asymptotically periodic). For this, the existence of solutions of the periodic case is first guaranteed using the Nehari manifold.
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