TY - JOUR
T1 - Periodic solutions of an infinite dimensional hamiltonian system
AU - Ding, Yanheng
AU - Lee, Cheng
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2005
Y1 - 2005
N2 - We establish existence and multiplicity of periodic solutions to the infinite dimensional Hamiltonian system (∂tu - Δxu = Hv(t, x, u, v) -∂tu - Δxu = Hv(t, x, u, v) for (t, x) ∈R × Ω, where Ω ⊂ RN is a bounded domain or Ω = RN. When Ω is bounded, we treat the situations where H(t, x, z) is, with respect to z = (u, v), sub- or superquadratic, or concave and convex, and discuss also the convergence to homoclinics of sequences of subharmonic orbits. If Ω = RN, we handle the case of superquadratic nonlinearities.
AB - We establish existence and multiplicity of periodic solutions to the infinite dimensional Hamiltonian system (∂tu - Δxu = Hv(t, x, u, v) -∂tu - Δxu = Hv(t, x, u, v) for (t, x) ∈R × Ω, where Ω ⊂ RN is a bounded domain or Ω = RN. When Ω is bounded, we treat the situations where H(t, x, z) is, with respect to z = (u, v), sub- or superquadratic, or concave and convex, and discuss also the convergence to homoclinics of sequences of subharmonic orbits. If Ω = RN, we handle the case of superquadratic nonlinearities.
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U2 - 10.1216/rmjm/1181069621
DO - 10.1216/rmjm/1181069621
M3 - Article
AN - SCOPUS:33645764606
VL - 35
SP - 1881
EP - 1908
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
SN - 0035-7596
IS - 6
ER -