First-order three-point BVPs at resonance (II)

First-order Three-Point BVPs at Resonance (II)

Abstract: This paper deals with existence of solutions to three-point BVPs in perturbed systems of first-order ordinary differential equations at resonance. An existence theorem is established by using the Theorem of Borsuk and some examples are given to illustrate it. A result for computing the local degree of polynomials whose terms of highest order have no common real linear factors is also ...

First-order three-point boundary value problems at resonance

Existence of Positive Solution to Second-Order Three-Point BVPs on Time Scales

We are concerned with the following nonlinear second-order three-point boundary value problem on time scales −xΔΔ t f t, x t , t ∈ a, b T , x a 0, x σ2 b δx η , where a, b ∈ T with a < b, η ∈ a, b T and 0 < δ < σ2 b − a / η − a . A new representation of Green’s function for the corresponding linear boundary value problem is obtained and some existence criteria of at least one positive solution ...

VARIABLE ORDER DIFFERENCE SCHEMES FOR NONLINEAR TWO-POINT BVPs

Two-point boundary value problems for a system of nonlinear first order ordinary differential equations are considered. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which possesses a prescribed order of accuracy O(|h|m) w.r.t. the maximal step size |h|. This m-TDS represen...

A Two-Stage LGSM for Three-Point BVPs of Second-Order ODEs

The study in this paper is a numerical integration of second-order three-point boundary value problems under two imposed nonlocal boundary conditions at t t0, t ξ, and t t1 in a general setting, where t0 < ξ < t1. We construct a two-stage Lie-group shooting method for finding unknown initial conditions, which are obtained through an iterative solution of derived algebraic equations in terms of ...