Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems
نویسندگان
چکیده
We are concerned with the higher-order nonlinear three-point boundary value problems: x n f t, x, x′, . . . , x n−1 , n ≥ 3, with the three point boundary conditions g x a , x′ a , . . . , x n−1 a 0; x i b μi, i 0, 1, . . . , n − 3;h x c , x′ c , . . . , x n−1 c 0, where a < b < c, f : a, c × R → R −∞, ∞ is continuous, g, h : R → R are continuous, andμi ∈ R, i 0, 1, . . . , n − 3 are arbitrary given constants. The existence and uniqueness results are obtained by using the method of upper and lower solutions together with Leray-Schauder degree theory. We give two examples to demonstrate our result.
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 کاملHigher order multi-point fractional boundary value problems with integral boundary conditions
In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...
متن کاملExistence and uniqueness of solutions for a periodic boundary value problem
In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.
متن کاملON SOLUTION OF A CLASS OF FUZZY BVPs
This paper investigates the existence and uniqueness of solutions to rst-order nonlinear boundary value problems (BVPs) involving fuzzy dif- ferential equations and two-point boundary conditions. Some sucient condi- tions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara dierentiability.
متن کاملExistence of positive solutions for fourth-order boundary value problems with three- point boundary conditions
In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009