This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order dynamic equations on time scales subject to two-point boundary conditions. The methods involve novel dynamic inequalities and fixed-point theory to yield new theorems guaranteeing the existence of at least one solution. AMS subject classification: 39A12, 34B15.

This article investigates the existence of solutions to first-order, nonlinear boundary value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point methods. AMS 2000 Classification: 34B15, 34B99

This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order ordinary differential equations and two-point, periodic boundary conditions. The methods involve novel differential inequalities and fixed-point theory to yield new theorems guaranteeing the existence of at least one solution. AMS 2000 Classification: 34B15

Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721–732], this article deals with the following discrete type BVP    ∆[φ(∆x(n))] + f(n, x(n + 1), ∆x(n), ∆x(n + 1)) = 0, n ∈ [0, N ], x(0)−mi=1 αix(ni) = A, x(N + 2)−mi=1 βix(ni) = B. The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem ...

Many boundary value problems (BVPs) or initial BVPs have non-smooth solutions, with jumps along lower-dimensional interfaces. The Explicit{Jump Immersed Interface Method (EJIIM) was developed following Li's Fast Iterative IIM (FIIIM), recognizing that the foundation for the eecient solution of many such problems is a good solver for elliptic BVPs. EJIIM generalizes the class of problems for whi...

Multipoint boundary value problems BVPs for second-order differential equations in a finite interval have been studied extensively and many results for the existence of solutions, positive solutions, multiple solutions are obtained by use of the Leray-Schauder continuation theorem, Guo-Krasnosel’skii fixed point theorem, and so on; for details see 1–4 and the references therein. In the last sev...

gðð yðaÞ; yðs2ðbÞÞ; yðeÞ; ð yDðaÞ; yDðsðbÞÞÞÞ 1⁄4 ð0; 0Þ; a , e , s2ðbÞ; e [ T; ð2Þ where f : 1⁄2a; b £ R! R; g : R £ R £ R ! R are continuous, and t is from a so-called “time scale” T. It is assumed that the reader is familiar with the time scale calculus and associated definitions such as delta derivative, jump operators and right-dense continuity. If not, then we refer the reader to Ref. [2]...

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t− 2) = a(t) f (x(t)), t ∈ [2,T], x(0)= x(T +2)=0, Δ2x(0)=Δ2x(T)=0 are established by using the well-known LeggettWilliams fixed point theorem, and then, for arbitrary positive integerm, existence results for at least 2m− 1 nonnegative solutions are ...

A family of fourth and second-order accurate numerical schemes is presented for the solution of nonlinear fourth-order boundary-value problems (BVPs) with two-point boundary conditions. Non-polynomial quintic spline functions are applied to construct the numerical algorithms. This approach generalizes nonpolynomial spline algorithms and provides a solution at every point of the range of integra...

The study of multipoint BVPs for linear second-order ordinary differential equations was initiated by Il’in and Moiseev 1 . Since then many authors studied more general nonlinear multipoint boundary value problems. We refer readers to 2–5 and the references therein. Motivated by works mentioned above, in this paper, we study the existence of positive solutions for the following second-order sin...