HOMOCLINIC SOLUTIONS FOR A CLASS OF AUTONOMOUS SECOND ORDER HAMILTONIAN SYSTEMS WITH A SUPERQUADRATIC POTENTIAL

作者：Janczewska Joanna^*

来源：Topological Methods in Nonlinear Analysis, 2010, 36(1): 19-26.

• Acution functional
• Hamiltonian system
• homoclinic solution
• general minimax principal
• superquardratic potential

We will prove the existence of a nontrivial homoclinic solution for an autonomous second order Hamiltonian system q + del V(q) = 0, where q is an element of R(n), a potential V: R(n) -> R is of the form V (q) = -K (q) + W (q), K and W are C(1)-maps, K satisfies the pinching condition, W grows at a superquadratic rate, as vertical bar q vertical bar -> infinity and W(q) = o(vertical bar q vertical bar(2)), as vertical bar q vertical bar -> 0. A homoclinic solution will be obtained as a weak limit in the Sobolev space W(1,2)(R, R(n)) of a sequence of almost critical points of the corresponding action functional. Before passing to a weak limit with a sequence of almost critical points each element of this sequence has to be appropriately shifted.

• 出版日期2010-9