Existence and multiplicity of homoclinic solutions for a second-order Hamiltonian system

Ye, Yiwei: Existence and multiplicity of homoclinic solutions for a second-order Hamiltonian system.

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Abstract

In this paper, we find new conditions to ensure the existence of one nontrivial homoclinic solution and also infinitely many homoclinic solutions for the second order Hamiltonian system u¨ − a(t)|u| p−2u + ∇W(t, u) = 0, t ∈ R, where p > 2, a ∈ C(R, R) with inft∈R a(t) > 0 and R R 1 a(t) �2/(p−2) dt < +∞, and W(t, x) is, as |x| → ∞, superquadratic or subquadratic with certain hypotheses different from those used in previous related studies. Our approach is variational and we use the Cerami condition instead of the Palais–Smale one for deformation arguments.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 11
ISSN: 1417-3875
Page Range: pp. 1-26
DOI: https://doi.org/10.14232/ejqtde.2019.1.11
Uncontrolled Keywords: Hamilton-rendszer
Additional Information: Bibliogr.: p. 23-26. ; összefoglalás angol nyelven
Date Deposited: 2019. May. 31. 06:22
Last Modified: 2020. Jul. 29. 12:24
URI: http://acta.bibl.u-szeged.hu/id/eprint/58106

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