New existence of homoclinic orbits for a second-order Hamiltonian system

作者：Chen, Peng; Tang, X. H.^*

来源：Computers & Mathematics with Applications, 2011, 62(1): 131-141.

DOI：10.1016/j.camwa.2011.04.060

• Homoclinic solutions
• Hamiltonian system
• Variational methods
• Weighted L(p) spaces

By using the Mountain Pass Theorem and the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee that the second-order Hamiltonian system u(t) - a(t)vertical bar u(t)vertical bar(p-2)u(t) + del W (t, u(t)) = 0 has at least one or infinitely many homoclinic orbits, where t is an element of R. u is an element of R(N), a is an element of C(R, R) and W is an element of C(1) (R x R(N), R) are not periodic in t. Our conditions on the potential W(t, x) are rather relaxed.

• 出版日期2011-7
• 单位中南大学