Publication result detail

Two-point boundary value problems for 4th order ordinary differential equations

MANJIKASHVILI, M.; MUKHIGULASHVILI, S.

Original Title

Two-point boundary value problems for 4th order ordinary differential equations

English Title

Two-point boundary value problems for 4th order ordinary differential equations

Type

WoS Article

Original Abstract

The new optimal efficient sufficient conditions are established for solvability and uniqueness of a solution of the linear and nonlinear fourth order ordinary differential equations u ( 4 ) ( t ) = p ( t ) u ( t )+ q ( t ) for t E [ a , b ] , u ( 4 ) ( t ) = p ( t ) u ( t ) + f ( t , u ( t )) for t E [ a , b ] , under the following two -point boundary conditions u ( i ) ( a ) = 0 , u ( i ) ( b ) = 0 ( i = 0 , 1 ) , and u ( i ) ( a ) = 0 ( i = 0 , 1 , 2 ) , u ( b ) = 0 , where p E L ([ a , b ] ; R ) is a nonconstant sign function and f E K ([ a , b ] x R; R ) .

English abstract

The new optimal efficient sufficient conditions are established for solvability and uniqueness of a solution of the linear and nonlinear fourth order ordinary differential equations u ( 4 ) ( t ) = p ( t ) u ( t )+ q ( t ) for t E [ a , b ] , u ( 4 ) ( t ) = p ( t ) u ( t ) + f ( t , u ( t )) for t E [ a , b ] , under the following two -point boundary conditions u ( i ) ( a ) = 0 , u ( i ) ( b ) = 0 ( i = 0 , 1 ) , and u ( i ) ( a ) = 0 ( i = 0 , 1 , 2 ) , u ( b ) = 0 , where p E L ([ a , b ] ; R ) is a nonconstant sign function and f E K ([ a , b ] x R; R ) .

Keywords

fourth order nonlinear ordinary differential equation; solvability; boundary value problem

Key words in English

fourth order nonlinear ordinary differential equation; solvability; boundary value problem

Authors

MANJIKASHVILI, M.; MUKHIGULASHVILI, S.

RIV year

2025

Released

01.05.2024

Publisher

University of Miskolc

ISBN

1787-2413

Periodical

Miskolc Mathematical Notes

Volume

25

Number

1

State

Hungary

Pages from

339

Pages to

409

Pages count

11

URL

http://mat76.mat.uni-miskolc.hu/mnotes/article/4481

Full text in the Digital Library

http://hdl.handle.net/11012/249492

BibTex

@article{BUT189515,
  author="Mariam {Manjikashvili} and Sulkhan {Mukhigulashvili}",
  title="Two-point boundary value problems for 4th order ordinary differential equations",
  journal="Miskolc Mathematical Notes",
  year="2024",
  volume="25",
  number="1",
  pages="339--409",
  doi="10.18514/MMN.2024.4481",
  issn="1787-2405",
  url="http://mat76.mat.uni-miskolc.hu/mnotes/article/4481"
}

Documents

4481