SOLUTION OF SPLIT BOUNDARY VALUE PROBLEMS

A function x t ∈ C ld 0 , 1 T ∩ C Δ ld ∇ 0 , 1 T is called a C ld 0 , 1 T positive solution of 1.1 if it satisfies 1.1 x t > 0 , for t ∈ 0 , 1 T ; if even x Δ 0 , x Δ 1 − exist, we call it is a C Δ ld 0 , 1 T solution.
To the best of our knowledge,[r]

operator σ : T → T by σt inf{ s ∈ T : s > t } and the backward jump operator ρ : T → T
by ρt sup{ s ∈ T : s < t }. If σt > t , t is said to be right scattered, and if σt t , t is said to be right dense. If ρt < t , t is said to be left scattered, and if ρt t , t is said to be left[r]

1. Introduction
The theory of di ff erential inclusions has received much attention due to its versatility and generality. For example, di ff erential inclusions can accurately model discontinuous pro- cesses, such as systems with dry friction; the work of an electric oscillator; and a[r]

VALUE PROBLEMS ON TIME SCALES
FORDYCE A. DAVIDSON AND BRYAN P. RYNNE
Received 6 February 2006; Revised 21 April 2006; Accepted 15 May 2006
We reconsider the basic formulation of second-order, two-point, Sturm-Liouville-type boundary value problems on[r]

14.4.2-2. Conditions of compatibility of initial and boundary conditions.
Suppose the function w has a continuous derivative with respect to t and two continuous derivatives with respect to x and is a solution of problem (14.4.2.1), (14.4.1.2), (14.4.1.3). Then t[r]

Because of applications in many areas for difference equations, in recent years, there has been an increased interest in studying of fourth-order difference equation, which include results on periodic solutions 11 , results on oscillation 12 – 14 , and results on boundary value[r]

4 , Jiang et al. 5 , and Torres 6 . Moreover, the positiveness of Green’s function implies that an antimaximum principle holds, which is a fundamental tool in the development of the monotone iterative technique; see Cabada et al. 7 and Torres and Zhang 8 .
The classical con[r]

Methods & Applications, vol. 69, no. 10, pp. 3291–3298, 2008.
21 A. V. Bicadze and A. A. Samarski˘ ı , “Some elementary generalizations of linear elliptic boundary value
problems,” Doklady Akademii Nauk SSSR, vol. 185, pp. 739–740, 1969.
22 C. P. Gupta, “A sec[r]

Copyright q 2011 Peiguo Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
By using the cone theory and the Banach contraction[r]

i 1 β i > 1 . In this paper, nonlinear terms f and g may be singular at t 0 , x, y θ , and/or
x , y θ , where θ denotes the zero element of Banach space E . By singularity, we mean that
f t, x 0 , x 1 , y 0 , y 1 → ∞ as t → 0 or x i , y i → θ i 0 , 1 .
Very recently, by[r]

t − ϕ

− ln t − ϕ .
Why have we written L ( t, ϕ ) in the form given in Equation 3.4.25? It clearly shows that the integral equation, Equation 3.4.23, contains a weakly singular kernel. Consequently, the finite difference representation of the inte- gral in Equation 3.4.24 consists o[r]

Copyright q 2011 E. K. Lee and Y.-H. Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper studies the existence, and mul[r]

Then BVP 4.1 has at least one solution on 0, π/2 according to Theorem 3.3 .
Acknowledgments
This work was supported by the Natural Science Foundation of China 10971173 , the Natural Science Foundation of Hunan Province 10JJ3096 , the Aid Program for Science and Techn[r]

Since many free boundary problems and obstacle problems may be reduced to partial differential equations with discontinuous nonlinearities, the existence of multiple solu- tions for Dirichlet boundary value problems with discontinuous nonlinearities h[r]

VALUE PROBLEM ON A TIME SCALE
BASANT KARNA AND BONITA A. LAWRENCE
Received 31 January 2006; Revised 15 April 2006; Accepted 19 April 2006
We will expand the scope of application of a fixed point theorem due to Krasnosel’ski˘ı and Zabreiko to the family of second-o[r]

Using fixed point index theory, we obtain several su ffi cient conditions of existence of at least one positive solution for third-order m -point boundary value problems.
Copyright © 2007 W. Jiang and F. Li. This is an open access article distributed under t[r]

Using fixed point index theory, we obtain several su ffi cient conditions of existence of at least one positive solution for third-order m -point boundary value problems.
Copyright © 2007 W. Jiang and F. Li. This is an open access article distributed under t[r]

We consider the existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive integrodi ff erential equations of mixed-type on time scales by establishing a comparison result and using the monotone iterative techniqu[r]

0 , ∞ × 0 , ∞ → 0 , ∞ are continuous and may be singular at t 0 , t 1 , x 0, and/or y 0, while the parameters η , α satisfy η ∈ 0 , 1 , 0 < α < 1 /η . An example is also included to show the applicability of our result.
Copyright q 2009 N. A. Asif and R. A. Khan. This is a[r]

1. Introduction
Multipoint boundary value problems BVPs for second-order di ff erential 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 th[r]