Abstract
AbstractThis paper is concerned with the global existence of solutions for the
semilinear nonlocal fractional Cauchy problem of the Schrödinger equation. Firstly,
based on the Schrödinger approximation technique and the theory of a family of
potential wells, the authors obtain the invariant sets and vacuum isolating of
global solutions including the critical case. Then, the global existence of
solutions and the stability of equilibrium points are discussed. Finally, the global
asymptotic stability of the unique positive equilibrium point of the system is
proved by applying the Leray–Schauder alternative fixed point theorem.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference33 articles.
1. Coti Zelati, V., Rabinowitz, P.H.: Homoclinic type solutions for a
semilinear elliptic PDE on $R^{n}$. Commun. Pure Appl. Math. 45,
1217–1269 (1992)
2. Kryszewski, W., Szulkin, A.: Generalized linking theorem with an
application to semilinear Schrödinger equation. Adv. Differ. Equ. 3, 441–472 (1998)
3. Kopidakis, G., Aubry, S., Tsironis, G.P.: Targeted energy transfer
through discrete breathers in nonlinear systems. Phys. Rev. Lett. 87, 165501 (2001)
4. Christodoulides, D.N., Lederer, F., Silberberg, Y.: Discretizing
light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817–823 (2003)
5. Fleischer, J.W., Carmon, T., Segev, M., Efremidis, N.K.,
Christodoulides, D.N.: Observation of discrete solitons in optically induced
real time waveguide arrays. Phys. Rev. Lett. 90, 023902 (2003)
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