Nonlinear Sum Operator Equations with a Parameter and Application to Second-Order Three-Point BVPs

Three Positive Solutions of Multi-point BVPs for Difference Equations with the Nonlinearity Depending on ∆−operator∗

This article deals with a class of discrete type boundary value problems. Sufficient conditions guaranteeing the existence of at least three positive solutions of this class of boundary value problems are established by using a fixed point theorem in cones in Banach spaces. An example is given to illustrate the main theorem.

Some Remarks on Three-point and Four-point Bvp’s for Second-order Nonlinear Differential Equations

We are interested in the existence of a positive solution to the four-point boundary value problem

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

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 ...

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 ...