TY - JOUR
T1 - Homoclinic orbits in a first order superquadratic hamiltonian system
T2 - Convergence of subharmonic orbits
AU - Tanaka, Kazunaga
PY - 1991/12
Y1 - 1991/12
N2 - We consider the existence of homoclinic orbits for a first order Hamiltonian system z ̇ = JHz(t, z). We assume H(t, z) is of form H(t, z) = 1 2(Az, z) + W(t, z), where A is a symmetric matrix with δ(JA)∩iR = ∅ and W(t, z) is 2π-periodic in t and has superquadratic growth in z. We prove the existence of a nontrivial homoclinic solution z∞(t) and subharmonic solutions (zT(t))Tε{lunate}N (i.e., 2πT-periodic solutions) of (HS) such that ZT(t) → Z∞(t) in Cloc1(R,R2N) as T → ∞.
AB - We consider the existence of homoclinic orbits for a first order Hamiltonian system z ̇ = JHz(t, z). We assume H(t, z) is of form H(t, z) = 1 2(Az, z) + W(t, z), where A is a symmetric matrix with δ(JA)∩iR = ∅ and W(t, z) is 2π-periodic in t and has superquadratic growth in z. We prove the existence of a nontrivial homoclinic solution z∞(t) and subharmonic solutions (zT(t))Tε{lunate}N (i.e., 2πT-periodic solutions) of (HS) such that ZT(t) → Z∞(t) in Cloc1(R,R2N) as T → ∞.
UR - http://www.scopus.com/inward/record.url?scp=38149144312&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38149144312&partnerID=8YFLogxK
U2 - 10.1016/0022-0396(91)90095-Q
DO - 10.1016/0022-0396(91)90095-Q
M3 - Article
AN - SCOPUS:38149144312
SN - 0022-0396
VL - 94
SP - 315
EP - 339
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -