Nonlinear boundary value problems and periodic solutions of ordinary differential equations : the Italian legacy (original) (raw)

A Note on the Existence of Periodic Solutions of Second Order Non-Linear Differential Equations

American Journal of Mathematics and Statistics, 2012

Bahman Mehri, using Leray-Schauder fixed point continuation method, established the existence of periodic solutions to equations of the form, x // +(k+h(x)) x / + f(t, x) = p(t),where h is a continuous function, f, p are continuous functions in their respective arguments and periodic with respect to t of period ω and k is a constant.The aim of this research is to extend this result to a wider class of equations of the form, x // +(k+h(x)) x / + F(t, x, x /) = p(t),where F is continuous in t,x and x / ; and periodic with respect to t of period ω and k is a constant, using Leray-Schauder fixed point continuation method.

APPROXIMATION AND RAPID CONVERGENCE OF SOLUTIONS FOR PERIODIC NONLINEAR PROBLEMS

2008

We study existence and approximation of solutions of some second order nonlinear periodic boundary value problem of the type x00(t) = f(t; x; x0); t 2 (0; T ); x(0) = x(T ); x0(0) = x0(T ); in the presence of lower and upper solutions. We develop the upper and lower solutions method and the quasilinearization technique for the existence and approximation of solutions. We apply our theoretical results to a medical problem.

A continuation theorem for periodic boundary value problems with oscillatory nonlinearities

Nodea-nonlinear Differential Equations and Applications - NODEA-NONLINEAR DIFFER EQU AP, 1995

We prove a continuation theorem for the solvability of the coincidence equationLx=Nx in normed spaces. Applications are given to the periodic boundary value problem for second order ordinary differential equations. Dealing, in particular, with the periodically forced Duffing equation