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Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems

✍ Scribed by Andrzej Szulkin; Wenming Zou

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
320 KB
Volume
187
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study the existence of homoclinic orbits for first order time-dependent Hamiltonian systems z Λ™=JH z (z, t), where H(z, t) depends periodically on t and H z (z, t) is asymptotically linear in z as |z| Q .. We also consider an asymptotically linear SchrΓΆdinger equation in R N .

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We study the existence of even homoclinic orbits for the second-order Hamiltonian system ΓΌ+V u (t, u) = 0. Let V(t, u) = -K(t, u)+W(t, u) ∈ C 1 (RΓ—R n , R), where K is less quadratic and W is super quadratic in u at infinity. Since the system we considered is neither autonomous nor periodic, the (PS