Approximating positive solutions of nonlinear BVPs of ordinary second order hybrid differential equations

Approximating positive solutions of nonlinear first order ordinary quadratic differential equations

Abstract: In this paper, the authors prove the existence as well as approximations of the positive solutions for an initial value problem of first-order ordinary nonlinear quadratic differential equations. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations converges monotonically to the positive solution of related quadratic differential e...

Throughout Positive Solutions of Second-order Nonlinear Differential Equations

In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations (a(t)x′(t))′ + f(t, x(g(t))) = 0, t ≥ t0 (a(t)(x(t)− p(t)x(t− τ))′)′ + f(t, x(g(t))) = 0, t ≥ t0 . Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.

EXISTENCE AND NON-EXISTENCE OF POSITIVE SOLUTIONS OF FOUR-POINT BVPs FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS ON WHOLE LINE

This paper is concerned with four-point boundary value problems of second order singular differential equations on whole lines. The Green’s function G(t, s) for the problem −(ρ(t)x′(t))′ = 0, lim t→−∞ ρ(t)x′(t)− kx(ξ) = lim t→+∞ ρ(t)x′(t) + lx(η) = 0 is obtained. We proved that G(t, s) ≥ 0 under some assumptions which actually generalizes a corresponding result in [Appl. Math. Comput. 217(2)(20...

C-approximate Solutions of Second-order Singular Ordinary Differential Equations

In this work a new method is developed to obtain C1-approximate solutions of initial and boundary-value problems generated from a one parameter second order singular ordinary differential equation. Information about the order of approximation is also given by introducing the so called growth index of a function. Conditions are given for the existence of such approximations for initial and bound...

Positive Periodic Solutions of Systems of Second Order Ordinary Differential Equations