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1997 On the existence of homoclinic orbits for a second-order Hamiltonian system
Addolorata Salvatore
Differential Integral Equations 10(2): 381-392 (1997).

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.

Citation

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Addolorata Salvatore. "On the existence of homoclinic orbits for a second-order Hamiltonian system." Differential Integral Equations 10 (2) 381 - 392, 1997.

Information

Published: 1997
First available in Project Euclid: 2 May 2013

zbMATH: 0894.34043
MathSciNet: MR1424818

Subjects:
Primary: 34C37
Secondary: 58F05

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.10 • No. 2 • 1997
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