In this paper, we study the existence of infinitely many homoclinic solutions for a class of first order Hamiltonian systems $\dot{z}=JH_z(t,z)$, where the Hamiltonian function $H$ possesses the form $H(t,z)=\frac{1}{2}L(t)z\cdot z +G(t,z)$, and $G(t,z)$ is only locally defined near the origin with respect to $z$. Under some mild conditions on $L$ and $G$, we show that the existence of a sequence of homoclinic solutions is actually a local phenomenon in some sense, which is essentially forced by the subquadraticity of $G$ near the origin with respect to $z$.
Qingye Zhang
,
Chungen Liu
. HOMOCLINIC SOLUTIONS NEAR THE ORIGIN FOR A CLASS OF FIRST ORDER HAMILTONIAN SYSTEMS*[J]. Acta mathematica scientia, Series B, 2023
, 43(3)
: 1195
-1210
.
DOI: 10.1007/s10473-023-0312-3
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