Criteria for the unique solution of two-point boundary value problems for an ordinary n-TH order differential equation

1969 ◽  
Vol 10 (2) ◽  
pp. 321-327 ◽  
Author(s):  
V. A. Churikov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Unique Solution ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

scholarly journals A note on solvability of three-point bound-ary value problems for third-order differential equations with p-Laplacian

2008 ◽  
Vol 39 (1) ◽  
pp. 95-103
Author(s):  
XingYuan Liu ◽  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Third Order ◽  
Third Order Differential Equation

Third-point boundary value problems for third-order differential equation$ \begin{cases} & [q(t)\phi(x''(t))]'+kx'(t)+g(t,x(t),x'(t))=p(t),\;\;t\in (0,1),\\ &x'(0)=x'(1)=x(\eta)=0. \end{cases} $is considered. Sufficient conditions for the existence of at least one solution of above problem are established. Some known results are improved.

scholarly journals Uniqueness intervals and two–point boundary value problems

2009 ◽  
Vol 43 (1) ◽  
pp. 91-97
Author(s):  
Grant B. Gustafson
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Graphical Representation ◽  
Boundary Value ◽  
Conjugate Function ◽  
Point Boundary ◽  
System Of Differential Equations ◽  
Linear Homogeneous Differential Equation

Abstract Consider a linear nth order differential equation with continuous coefficients and continuous forcing term. The maximal uniqueness interval for a classical 2-point boundary value problem will be calculated by an algorithm that uses an auxiliary linear system of differential equations, called a Mikusinski system. This system always has higher order than n. The algorithm leads to a graphical representation of the uniqueness profile and to a new method for solving 2-point boundary value problems. The ideas are applied to construct a graphic for the conjugate function associated with the nth order linear homogeneous differential equation. Details are given about how to solve classical 2-point boundary value problems, using auxiliary Mikusinski systems and Green’s function.

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

1997 ◽  
Vol 4 (6) ◽  
pp. 557-566
Author(s):  
B. Půža
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Vector Function ◽  
Unique Solvability ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Deviating Arguments ◽  
Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS

2004 ◽  
Vol 02 (01) ◽  
pp. 71-85 ◽  
Author(s):  
YUJI LIU ◽  
WEIGAO GE
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Order Ordinary Differential Equation ◽  
Order Four

In this paper, we study four-point boundary value problems for a fourth-order ordinary differential equation of the form [Formula: see text] with one of the following boundary conditions: [Formula: see text] or [Formula: see text] Growth conditions on f which guarantee existence of at least three positive solutions for the problems (E)–(B1) and (E)–(B2) are imposed.

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