Uniqueness implies existence for three-point boundary value problems for dynamic equations
نویسندگان
چکیده
K e y w o r d s T i m e scale, Boundary value problem, Dynamic equation, Shooting method. 1. I N T R O D U C T I O N This paper is devoted to boundary value problems for dynamic equations on time scales. It is assumed that , by this time in the development of the theory, the reader is familiar with time scale calculus and notation for delta differentiation, as well as concepts for dynamic equations on time scales. Otherwise, the reader is referred to the introductory book on time scales by Bohner and Peterson [1]. Let T be a nonempty closed subset of ]~ (i.e., ~F is a time scale), with endpoints a < b. For notation, we use the convention that, for each subset S of ]~,
منابع مشابه
Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کاملExistence of positive solution to a class of boundary value problems of fractional differential equations
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...
متن کاملExistence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0
متن کاملPeriodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces
This paper deals with the Periodic boundary value problems for Controlled nonlinear impulsive evolution equations. By using the theory of semigroup and fixed point methods, some conditions ensuring the existence and uniqueness. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.
متن کاملApplied Mathematics Report Amr03/33 Uniqueness Implies Existence for Three-point Boundary Value Problems for Second Order Dynamic Equations
Shooting methods are used to obtain solutions of the three-point boundary value problem for the second order dynamic equation, y = f(x, y, y), y(x1) = y1, y(x3) − y(x2) = y2, where f : (a, b)T × R → R is continuous , x1 < x2 < x3 in (a, b)T, y1, y2 ∈ R, and T is a time scale. It is assumed such solutions are unique when they exist. 2000 AMS Subject Classification: 39B10
متن کاملExistence and uniqueness results for a nonlinear differential equations of arbitrary order
This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 17 شماره
صفحات -
تاریخ انتشار 2004