Higher monotonicity properties of zero points of the linear combination of the solution and its first derivative of the differential equation
We establish Hille-Wintner type comparison criteria for the half-linear second order differential equation where this equation is viewed as a perturbation of another equation of the same form.
We consider a conservative second order Hamiltonian system in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.