Title: Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition
Abstract: We study the existence and multiplicity of homoclinic orbits for second‐order Hamiltonian systems , where L ( t ) is unnecessarily positive definite for all t ∈ ℝ , and ∇ q W ( t , q ) is of at most linear growth and satisfies some twist condition between the origin and the infinity.