naa a22 4500 510782213 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0016-9 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0016-9 Ground state periodic solutions of second order Hamiltonian systems without spectrum 0 [Elektronische Daten] [Guanwei Chen, Shiwang Ma] In this paper, we consider the second order Hamiltonian system $\left\{ \begin{gathered} u''(t) + A(t)u(t) + \nabla H(t,u(t)) = 0,t \in R, \hfill \\ u(0) = u(T),u'(0) = u'(T),T > 0. \hfill \\ \end{gathered} \right.$ Here, we assume 0 lies in a gap of σ(B) (the spectrum of B:= −d 2/dt 2 −A(t)). We find nontrivial and ground state T-periodic solutions for the second order Hamiltonian system under conditions weaker than those previously assumed; also, our proof is much more direct. Hebrew University Magnes Press, 2013 Chen Guanwei School of Mathematics and Statistics, Anyang Normal University, 455000, Anyang, Henan Province, P.R. China aut Ma Shiwang School of Mathematical Sciences and LPMC, Nankai University, 300071, Tianjin, P. R. China aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 111-127 0021-2172 198:1<111 2013 198 11856 https://doi.org/10.1007/s11856-013-0016-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0016-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Guanwei School of Mathematics and Statistics, Anyang Normal University, 455000, Anyang, Henan Province, P.R. China aut NATIONALLICENCE 700 1- Ma Shiwang School of Mathematical Sciences and LPMC, Nankai University, 300071, Tianjin, P. R. China aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 111-127 0021-2172 198:1<111 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer