We prove the existence of infinitely many homoclinic solutions for a class of second order hamiltonian systems of the form $-\ddot u+u=\alpha(t)\nabla W(u)$ where $W$ is superquadratic and $\dot\alpha(t)\to 0$, $0<\liminf\alpha(t)<\limsup\alpha(t)$ as $t\to +\infty$. In fact we prove that such a kind of systems admit a ``multibump'' dynamics
Multibump solutions for a class of Lagrangian systems slowly oscillating at infinity / Alessio, FRANCESCA GEMMA; Montecchiari, Piero. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 16:1(1999), pp. 107-135. [10.1016/S0294-1449(99)80009-2]
Multibump solutions for a class of Lagrangian systems slowly oscillating at infinity
ALESSIO, FRANCESCA GEMMA;MONTECCHIARI, Piero
1999-01-01
Abstract
We prove the existence of infinitely many homoclinic solutions for a class of second order hamiltonian systems of the form $-\ddot u+u=\alpha(t)\nabla W(u)$ where $W$ is superquadratic and $\dot\alpha(t)\to 0$, $0<\liminf\alpha(t)<\limsup\alpha(t)$ as $t\to +\infty$. In fact we prove that such a kind of systems admit a ``multibump'' dynamicsFile in questo prodotto:
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