## Differential and Integral Equations

### On the existence of homoclinic orbits for a second-order Hamiltonian system

#### Abstract

In this paper we look for homoclinic solutions of the system $$\ddot q-a(t)\mid q\mid ^{p-2}q+W_q(t,q)=0$$ where $p>2,$ $a(t)\rightarrow +\infty$ as $\mid q\mid \rightarrow +\infty$ and $W(t,\cdot )$ is even and quadratic or superquadratic at infinity and at the origin. Using a compact embedding between suitable weighted Sobolev spaces, we prove the existence of infinitely many homoclinic solutions of the problem.

#### Article information

Source
Differential Integral Equations, Volume 10, Number 2 (1997), 381-392.

Dates
First available in Project Euclid: 2 May 2013

https://projecteuclid.org/euclid.die/1367526344

Mathematical Reviews number (MathSciNet)
MR1424818

Zentralblatt MATH identifier
0894.34043

Subjects
Primary: 34C37: Homoclinic and heteroclinic solutions
Secondary: 58F05

#### Citation

Salvatore, Addolorata. On the existence of homoclinic orbits for a second-order Hamiltonian system. Differential Integral Equations 10 (1997), no. 2, 381--392. https://projecteuclid.org/euclid.die/1367526344