The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation

被引：0

作者：

Efendiev, B. I. ^{[1
]}

机构：

[1] Inst Appl Math & Automat, Nalchik, Russia

来源：

MATHEMATICAL NOTES | 2018年 / 103卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

continuous differential equation; fractional integro-differential operator; Dirichlet problem; extremum principle;

D O I：

10.1134/S0001434618010297

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The extremum principle for an ordinary continuous second-order differential equation with variable coefficients is proved and this principle is used to establish the uniqueness of the solution of the Dirichlet problem. The problem under consideration is equivalently reduced to the Fredholm integral equation of the second kind and the unique solvability of this integral equation is proved.

引用

页码：290 / 296

页数：7

共 50 条

[1] The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation
B. I. Éfendiev
[J]. Mathematical Notes, 2018, 103 : 290 - 296
[2] On the Dirichlet problem for vector second-order ordinary differential eguations
Filippov, VV
[J]. DIFFERENTIAL EQUATIONS, 1997, 33 (08) : 1063 - 1074
[3] On the Dirichlet problem for a second-order ordinary differential equation with discontinuous right-hand side
Zuev, AV
[J]. DIFFERENTIAL EQUATIONS, 2006, 42 (03) : 340 - 346
[4] On the Dirichlet problem for a second-order ordinary differential equation with discontinuous right-hand side
A. V. Zuev
[J]. Differential Equations, 2006, 42 : 340 - 346
[5] Dirichlet problem for second-order ordinary differential equations with segment-order derivative
B. I. Éfendiev
[J]. Mathematical Notes, 2015, 97 : 632 - 640
[6] Dirichlet problem for second-order ordinary differential equations with segment-order derivative
Efendiev, B. I.
[J]. MATHEMATICAL NOTES, 2015, 97 (3-4) : 632 - 640
[7] Cauchy Problem for a Second-Order Ordinary Differential Equation with a Continual Derivative
Efendiev, B. I.
[J]. DIFFERENTIAL EQUATIONS, 2011, 47 (09) : 1378 - 1383
[8] Steklov problem for a second-order ordinary differential equation with a continual derivative
Efendiev, B. I.
[J]. DIFFERENTIAL EQUATIONS, 2013, 49 (04) : 450 - 456
[9] Cauchy problem for a second-order ordinary differential equation with a continual derivative
B. I. Efendiev
[J]. Differential Equations, 2011, 47 : 1378 - 1383
[10] Steklov problem for a second-order ordinary differential equation with a continual derivative
B. I. Efendiev
[J]. Differential Equations, 2013, 49 : 450 - 456

← 1 2 3 4 5 →