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Zubiaga, W., (2022). Existencia de solución para un sistema Hamiltoniano Fraccionario [Universidad Nacional de Trujillo]. https://hdl.handle.net/20.500.14414/19259
Zubiaga, W., Existencia de solución para un sistema Hamiltoniano Fraccionario []. PE: Universidad Nacional de Trujillo; 2022. https://hdl.handle.net/20.500.14414/19259
@phdthesis{renati/1046985,
title = "Existencia de solución para un sistema Hamiltoniano Fraccionario",
author = "Zubiaga Vera, Willy Frank",
publisher = "Universidad Nacional de Trujillo",
year = "2022"
}
Title: Existencia de solución para un sistema Hamiltoniano Fraccionario
Authors(s): Zubiaga Vera, Willy Frank
Advisor(s): Torres Ledesma, César Enrique
Keywords: Sistema hamiltoniano fraccionario; Espacios fraccionarios; Métodos variacionales; Teorema del paso de la montaña
OCDE field: https://purl.org/pe-repo/ocde/ford#1.01.00
Issue Date: 2022
Institution: Universidad Nacional de Trujillo
Abstract: En este trabajo se considera la existencia de solución débil para un sistema Hamiltoniano
fraccionario de la forma
(P) tD↵1(−1D↵
t u(t)) + L(t)u(t) = rW(t, u(t))
donde ↵ 2 (1/2, 1), L 2 C(R,Rn2) es una matriz sim´etrica positiva definida, W(t, u) =
a(t)V (t) con a 2 C(R,R+) y V 2 C1(Rn,R). Suponiendo que existe una constanteM > 0
tal que (L(t)u, u) # M|u|2 para todo (t, u) 2 R ⇥ Rn y V satisface la condici´on global de
Ambrosetti-Rabinowitz y otras condiciones adecuadas, se demuestra la existencia de una solución débil para (P), al usar el teorema del paso de la montaña.
In this work we deal with the existence of weak solution for the fractional Hamiltonian systems (P) tD↵1(−1D↵ t u(t)) + L(t)u(t) = rW(t, u(t)) where ↵ 2 (1/2, 1), L 2 C(R,Rn2) is a symmetric and positive definite matrix, W(t, u) = a(t)V (t) with a 2 C(R,R+) and V 2 C1(Rn,R). Assuming that there is a constantM > 0 such that (L(t)u, u) # M|u|2 for all (t, u) 2 R ⇥ Rn and V satisfies the global Ambrosetti- Rabinowitz condition and other suitable conditions, we show the existence of one nontrivial weak solution to (P), by using the Mountain pass theorem.
In this work we deal with the existence of weak solution for the fractional Hamiltonian systems (P) tD↵1(−1D↵ t u(t)) + L(t)u(t) = rW(t, u(t)) where ↵ 2 (1/2, 1), L 2 C(R,Rn2) is a symmetric and positive definite matrix, W(t, u) = a(t)V (t) with a 2 C(R,R+) and V 2 C1(Rn,R). Assuming that there is a constantM > 0 such that (L(t)u, u) # M|u|2 for all (t, u) 2 R ⇥ Rn and V satisfies the global Ambrosetti- Rabinowitz condition and other suitable conditions, we show the existence of one nontrivial weak solution to (P), by using the Mountain pass theorem.
Link to repository: https://hdl.handle.net/20.500.14414/19259
Discipline: Doctorado en Matemática
Grade or title grantor: Universidad Nacional de Trujillo. Escuela de Postgrado.
Grade or title: Doctor en Matemática
Juror: Méndez Cruz, Gilberto Amado; Maco Vásquez, Wilson Arcenio; Torres Ledesma, César Enrique
Register date: 2-Nov-2023
This item is licensed under a Creative Commons License