Existence results for a class of high order differential equation associated with integral boundary conditions at resonance

Le Cong Nhan; Do Huy Hoang; Le Xuan Truong

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 2, page 111-130
  • ISSN: 0044-8753

Abstract

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By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form x ( n ) = f ( t , x , x ' , ⋯ , x ( n - 1 ) ) , t ∈ [ 0 , 1 ] , associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.

How to cite

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Nhan, Le Cong, Hoang, Do Huy, and Truong, Le Xuan. "Existence results for a class of high order differential equation associated with integral boundary conditions at resonance." Archivum Mathematicum 053.2 (2017): 111-130. <http://eudml.org/doc/288196>.

@article{Nhan2017,
abstract = {By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form \[x^\{(n)\} =f(t,x,x^\{\prime \},\dots ,x^\{(n-1)\})\,, \quad t \in [0, 1]\,,\] associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.},
author = {Nhan, Le Cong, Hoang, Do Huy, Truong, Le Xuan},
journal = {Archivum Mathematicum},
keywords = {coincidence degree; high order differential equation; resonance},
language = {eng},
number = {2},
pages = {111-130},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence results for a class of high order differential equation associated with integral boundary conditions at resonance},
url = {http://eudml.org/doc/288196},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Nhan, Le Cong
AU - Hoang, Do Huy
AU - Truong, Le Xuan
TI - Existence results for a class of high order differential equation associated with integral boundary conditions at resonance
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 2
SP - 111
EP - 130
AB - By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form \[x^{(n)} =f(t,x,x^{\prime },\dots ,x^{(n-1)})\,, \quad t \in [0, 1]\,,\] associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.
LA - eng
KW - coincidence degree; high order differential equation; resonance
UR - http://eudml.org/doc/288196
ER -

References

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