Homoclinic Orbits of Nonperiodic Superquadratic Hamiltonian System
نویسندگان
چکیده
In this paper, we study the following first-order nonperiodic Hamiltonian system ż = JHz(t, z), where H ∈ C1(R× R ,R) is the form H(t, z) = 1 2 L(t)z · z + R(t, z). Under weak superquadratic condition on the nonlinearitiy. By applying the generalized Nehari manifold method developed recently by Szulkin and Weth, we prove the existence of homoclinic orbits, which are ground state solutions for above system.
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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