Fixed points and solutions of boundary value problems at resonance

Alaa Almansour; Paul Eloe

Annales Polonici Mathematici (2015)

  • Volume: 115, Issue: 3, page 263-274
  • ISSN: 0066-2216

Abstract

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We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a partial explanation as to why the contraction mapping principle is not a viable tool for boundary value problems at resonance.

How to cite

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Alaa Almansour, and Paul Eloe. "Fixed points and solutions of boundary value problems at resonance." Annales Polonici Mathematici 115.3 (2015): 263-274. <http://eudml.org/doc/280860>.

@article{AlaaAlmansour2015,
abstract = {We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a partial explanation as to why the contraction mapping principle is not a viable tool for boundary value problems at resonance.},
author = {Alaa Almansour, Paul Eloe},
journal = {Annales Polonici Mathematici},
keywords = {boundary value problem at resonance; green's functions; Fredholm alternative},
language = {eng},
number = {3},
pages = {263-274},
title = {Fixed points and solutions of boundary value problems at resonance},
url = {http://eudml.org/doc/280860},
volume = {115},
year = {2015},
}

TY - JOUR
AU - Alaa Almansour
AU - Paul Eloe
TI - Fixed points and solutions of boundary value problems at resonance
JO - Annales Polonici Mathematici
PY - 2015
VL - 115
IS - 3
SP - 263
EP - 274
AB - We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a partial explanation as to why the contraction mapping principle is not a viable tool for boundary value problems at resonance.
LA - eng
KW - boundary value problem at resonance; green's functions; Fredholm alternative
UR - http://eudml.org/doc/280860
ER -

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