Homoclinic orbits for Schrödinger systems



The Michigan Mathematical Journal

Homoclinic orbits for Schrödinger systems

Martin Schechter and Wenming Zou

Source: Michigan Math. J. Volume 51, Issue 1 (2003), 59-72.

Primary Subjects: 35Q55, 58E05, 35J65
Secondary Subjects: 58E05, 35Q55

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.mmj/1049832893
Digital Object Identifier: doi:10.1307/mmj/1049832893
Zentralblatt MATH identifier: 01943245

References

A. Ambrosetti and M. Badiale, Homoclinics: Poincaré--Melnikov type results via variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), 233--252.
Mathematical Reviews (MathSciNet): MR1614571
Digital Object Identifier: doi:10.1016/S0294-1449(97)89300-6
------, Variational perturbative methods and bifurcation of bound states from the essential spectrum, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), 1131--1161.
Mathematical Reviews (MathSciNet): MR1664089
T. Bartsch and Y. Ding, On a nonlinear Schrödinger equation with periodic potential, Math. Ann. 313 (1999), 15--37.
Mathematical Reviews (MathSciNet): MR1666801
Digital Object Identifier: doi:10.1007/s002080050248
------, Homoclinic solutions of an infinite-dimensional Hamiltonian systems, Math. Z. 240 (2002), 289--310.
Mathematical Reviews (MathSciNet): MR1900313
Digital Object Identifier: doi:10.1007/s002090100383
H. Brézis and L. Nirenberg, Characterization of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scoula Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), 225--326.
Mathematical Reviews (MathSciNet): MR513090
P. Clèment, P. Felmer, and E. Mitidieir, Homoclinic orbits for a class of infinite dimensional Hamiltonian systems, Ann. Scoula Norm. Sup. Pisa Cl. Sci. (4) 24 (1997), 367--393.
Mathematical Reviews (MathSciNet): MR1487960
V. Coti-Zelati and P. H. Rabinowitz, Homoclinic type solutions for a semilinear elliptic PDE on $\bold R^N,$ Comm. Pure Appl. Math. 45 (1992), 1217--1269.
Mathematical Reviews (MathSciNet): MR1181725
N. Dunford and J. T. Schwartz, Linear operators, part I, Interscience, New York, 1967.
L. Jeanjean, On the existence of bounded Palais--Smale sequences and application to a Landesman--Lazer type problem set on $\bold R^N,$ Proc. Roy. Soc. Edinburgh Sect. A 129 (1999), 787--809.
Mathematical Reviews (MathSciNet): MR1718530
W. Kryszewski and A. Szulkin, Generalized linking theorem with an application to a semilinear Schrödinger equation, Adv. Differential Equations 3 (1998), 441--472.
Mathematical Reviews (MathSciNet): MR1751952
P. L. Lions, The concentration-compactness principle in the calculus of variations: The locally compact case. Part II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 223--283.
Mathematical Reviews (MathSciNet): MR778974
M. Reed and B. Simon, Methods of modern mathematical physics, vol. IV, Academic Press, New York, 1978.
Mathematical Reviews (MathSciNet): MR493421
M. Schechter and W. Zou, Weak linking theorem and Schrödinger equations, Mathematika (to appear).
Mathematical Reviews (MathSciNet): MR2060524
A. Szulkin and W. Zou, Homoclinic orbits for asymptotically linear Hamiltonian systems, J. Funct. Anal. 187 (2001), 25--41.
Mathematical Reviews (MathSciNet): MR1867339
Digital Object Identifier: doi:10.1006/jfan.2001.3798
M. Willem and W. Zou, On a semilinear Dirichlet problem and a nonlinear Schrödinger equation with periodic potential, preprint.
W. Zou, Variant fountain theorems and their applications, Manuscripta Math. 104 (2001), 343--358.
Mathematical Reviews (MathSciNet): MR1828880
Digital Object Identifier: doi:10.1007/s002290170032

2008 © The University of Michigan