Sufficient conditions for the oscillation to bounded solutions of a class of impulsive differential equations of second order with a constant delay.
This paper is concerned with the existence of bounded or unbounded solutions to third-order boundary value problem on the half-line with functional boundary conditions. The arguments are based on the Green functions, a Nagumo condition, Schauder fixed point theorem and lower and upper solutions method. An application to a Falkner-Skan equation with functional boundary conditions is given to illustrate our results.
In the present paper we seek the bounce trajectories in a convex set which assume assigned positions in two fixed time instants. We find sufficient conditions in order to obtain the existence of infinitely many bounce trajectories.
This article studies the summability of first integrals of a -non-integrable resonant Hamiltonian system. The first integrals are expressed in terms of formal exponential transseries and their Borel sums. Smooth Liouville integrability and a relation to the Birkhoff transformation are discussed from the point of view of the summability.
The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.
We construct time quasi-periodic solutions and prove almost global existence for the energy supercritical nonlinear Schrödinger equations on the torus in arbitrary dimensions. The main new ingredient is a geometric selection in the Fourier space. This method is applicable to other nonlinear equations.