scholarly journals On Two-Point Boundary Value Problems for Systems of Higher-Order Ordinary Differential Equations with Singularities

1994 ◽  
Vol 1 (1) ◽  
pp. 31-45
Author(s):  
I. Kiguradze ◽  
G. Tskhovrebadze
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Vector Function ◽  
Unique Solvability ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Point Boundary

Abstract The sufficient conditions of solvability and unique solvability of the two-point boundary value problems of Vallèe-Poussin and Cauchy-Niccoletti have been found for a system of ordinary differential equations of the form u (n) = ƒ(t, u, u′, . . . , u (n – 1)), where the vector function has nonintegrable singularities with respect to the first argument at the points a and b.

On Some Two-Point Boundary Value Problems for Two-Dimensional Systems of Ordinary Differential Equations

1994 ◽  
Vol 1 (3) ◽  
pp. 303-314
Author(s):  
A. Lomtatidze
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Two Dimensional ◽  
Point Boundary

Abstract Sufficient conditions for the solvability of two-point boundary value problems for the system are given, where f 1 and f 2 : [a 1 , a 2] × R 2 → R are continuous functions.

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.

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.

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