Abstract
The existence of homoclinic solutions is obtained for a class of nonautonomous second order Hamiltonian systems $\ddot{u}(t)+\nabla V(t,u(t))=f(t)$ as the limit of the $2kT$-periodic solutions which are obtained by the Mountain Pass theorem, where $V(t,x)=-K(t,x)+W(t,x)$ is $T$-periodic with respect to $t,T>0$, and $W(t,x)$ satisfies the superquadratic condition: $W(t,x) / |x|^{2} \rightarrow +\infty$ as $|x| \rightarrow \infty$ uniformly in $t$, which needs not to satisfy the global Ambrosetti-Rabinowitz condition.
Citation
Dong-Lun Wu. Xing-Ping Wu. Chun-Lei Tang. "Homoclinic solutions for second order Hamiltonian systems with small forcing terms." Bull. Belg. Math. Soc. Simon Stevin 19 (4) 747 - 761, november 2012. https://doi.org/10.36045/bbms/1353695913
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