Existencia de solución para un sistema Hamiltoniano Fraccionario
No Thumbnail Available
Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
Keywords
Sistema hamiltoniano fraccionario, Espacios fraccionarios, Métodos variacionales, Teorema del paso de la montaña