Homoclinics for strongly indefinite almost periodic second order Hamiltonian systems-Reference-Cited by-同舟云学术

Homoclinics for strongly indefinite almost periodic second order Hamiltonian systems

Published:2017-04-19 Issue:1 Volume:8 Page:372-385
ISSN:2191-9496
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Pankov Alexander¹

Affiliation:

1. Department of Mathematics , Morgan State University , 1700 E. Cold Spring Lane , Baltimore , MD 21251 , USA ; and RUDN University, 6 Miklukho-Maklay St., Moscow 117198, Russia

Abstract

Abstract Under certain assumptions, we prove the existence of homoclinic solutions for almost periodic second order Hamiltonian systems in the strongly indefinite case. The proof relies on a careful analysis of the energy functional restricted to the generalized Nehari manifold, and the existence and fine properties of special Palais–Smale sequences.

Funder

Ministry of Education and Science of the Russian Federation

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference23 articles.

1. F. Alessio, M. L. Bertotti and P. Montecchiari, Multibump solutions to possibly degenerate equilibria for almost periodic Lagrangian systems, Z. Angew. Math. Phys. 50 (1999), 860–891.

2. F. Alessio and M. Calanchi, Homoclinic-type solutions for an almost periodic semilinear elliptic equation on ℝ n {\mathbb{R}^{n}} , Rend. Semin. Mat. Univ. Padova 97 (1997), 89–111.

3. G. Arioli and A. Szulkin, Homoclinic solutions for a class of systems of second order differential equations, Topol. Methods Nonlinear Anal. 6 (1995), 189–197.

4. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011.

5. V. Coti Zelatti, P. Montecchiari and M. Nolasco, Multibump homoclinic solutions for a class of second order, almost periodic Hamiltonian systems, NoDEA Nonlinear Differential Equations Appl. 4 (1997), 77–99.

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