ON A METHOD FOR SOLVING A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 73 (1) ◽  
pp. 70-75
Author(s):  
S.M. Temesheva ◽  
◽  
P.B. Abdimanapova ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Point Boundary ◽  
Local Boundary ◽  
The Family ◽  
Non Local

In this paper, we consider a boundary value problem for a family of linear differential equations that obey a family of nonlinear two-point boundary conditions. For each fixed value of the family parameter, the boundary value problem under study is a nonlinear two-point boundary value problem for a system of ordinary differential equations. Non-local boundary value problems for systems of partial differential equations, in particular, non-local boundary value problems for systems of hyperbolic equations with mixed derivatives, can be reduced to the family of boundary value problems for ordinary differential equations. Therefore, the establishment of solvability conditions and the development of methods for solving a family of boundary value problems for differential equations are actual problems. In this paper, using the ideas of the parametrization method of D. S. Dzhumabaev, which was originally developed to establish the signs of unambiguous solvability of a linear two-point boundary value problem for a system of ordinary equations, a method for finding a numerical solution to the problem under consideration is proposed.

scholarly journals ON THREE-POINT BOUNDARY VALUE PROBLEM

2016 ◽  
Vol 21 (2) ◽  
pp. 270-281
Author(s):  
Nadezhda Sveikate
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Point Boundary

Three-point boundary value problems for the second order nonlinear ordinary differential equations are considered. Existence of solutions are established by using the quasilinearization approach. As an application, the Emden-Fowler type problems with nonresonant and resonant linear parts are considered to demonstrate our results.

scholarly journals On the solvability of a semi-periodic boundary value problem for the nonlinear Goursat equation

2021 ◽  
Vol 104 (4) ◽  
pp. 110-117
Author(s):  
N.T. Orumbayeva ◽  
◽  
T.D. Tokmagambetova ◽  
Zh.N. Nurgalieva ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Periodic Problem ◽  
Periodic Boundary Value Problem ◽  
Functional Relations

In this paper, by means of a change of variables, a nonlinear semi-periodic boundary value problem for the Goursat equation is reduced to a linear gravity problem for hyperbolic equations. Reintroducing a new function, the obtained problem is reduced to a family of boundary value problems for ordinary differential equations and functional relations. When solving a family of boundary value problems for ordinary differential equations, the parameterization method is used. The application of this approach made it possible to establish the coefficients of the unique solvability of the semi-periodic problem for the Goursat equation and to propose constructive algorithms for finding an approximate solution.

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.

Existence theorems for equations in normed spaces and boundary value problems for nonlinear vector ordinary differential equations

1984 ◽  
Vol 98 (1-2) ◽  
pp. 1-11 ◽  
Author(s):  
A. Cañada ◽  
R. Ortega
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Linear Part ◽  
Sufficient Conditions ◽  
First Eigenvalue ◽  
Normed Spaces ◽  
Nonlinear Vector

SynopsisThe existence of solutions to equations in normed spaces is proved when the nonlinear part of the equation satisfies growth and asymptotic conditions, whether the linear part is invertible or not. For this, we use the coincidence degree theory developed by Mawhin. We apply our abstract results to boundary value problems for nonlinear vector ordinary differential equations. In particular, we consider the Picard boundary value problem at the first eigenvalue and the periodic boundary value problem at resonance. In both cases, the nonlinear term can be of superlinear type. Also, necessary and sufficient conditions of Landesman-Lazer type are obtained.

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