Bulletin of the Belgian Mathematical Society - Simon Stevin

Homoclinic solutions for second order Hamiltonian systems with small forcing terms

Dong-Lun Wu, Xing-Ping Wu, and Chun-Lei Tang

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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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 4 (2012), 747-761.

Dates
First available in Project Euclid: 23 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1353695913

Digital Object Identifier
doi:10.36045/bbms/1353695913

Mathematical Reviews number (MathSciNet)
MR3009034

Zentralblatt MATH identifier
1315.37039

Keywords
Homoclinic orbits Second order Hamiltonian systems $(C)$ condition Mountain pass theorem Superquadratic condition

Citation

Wu, Dong-Lun; Wu, Xing-Ping; Tang, Chun-Lei. Homoclinic solutions for second order Hamiltonian systems with small forcing terms. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 4, 747--761. doi:10.36045/bbms/1353695913. https://projecteuclid.org/euclid.bbms/1353695913


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