Existence of Homoclinic Orbits for Second Order Hamiltonian Systems without (ar) Condition
نویسنده
چکیده
The existence of homoclinic orbits is obtained for a class of the second order Hamiltonian systems ü(t)−L(t)u(t)+∇W (t,u(t)) = 0, ∀t ∈ R , by the mountain pass theorem, where W(t,x) needs not to satisfy the global (AR) condition. Mathematics subject classification (2000): 34C37, 37J45, 47J30, 58E05.
منابع مشابه
Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential
and Applied Analysis 3 Theorem 3. Assume that L satisfies (L) and (L) and W satisfies (W1), (W4), (W8) and (W9). Then problem (1) possesses a nontrivial homoclinic orbit. Remark 4. In Theorem 3, we consider the existence of homoclinic orbits for problem (1) under a class of local superquadratic conditions without the (AR) condition and any periodicity assumptions on both L and W. There are func...
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تاریخ انتشار 2009