Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition - Qi Wang; Qingye Zhang (Abstract and Applied Analysis, 2012)
We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems q¨−L(t)q+∇qW(t,q)=0, where L(t) is unnecessarily positive definite for all t∈ℝ, and ∇qW(t,q) is of at most linear growth and satisfies some twist condition between the origin and the infinity.