Differential and Integral Equations

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

Addolorata Salvatore

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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

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

First available in Project Euclid: 2 May 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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