Geodesic
Fixed points and solutions of boundary value problems at resonance
Alaa Almansour1 ; Paul Eloe1
1 Department of Mathematics University of Dayton Dayton, OH 45469-2316, U.S.A.
Annales Polonici Mathematici, Tome 115 (2015) no. 3, pp. 263-274

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap115-3-5
Keywords: consider simple boundary value problem resonance ordinary differential equation employ shift argument construct regular fixed point operator contrast current applications coincidence degree standard fixed point theorems applied sufficient conditions existence solutions provide three applications fixed point theory delicate application contraction mapping principle notably missing partial explanation why contraction mapping principle viable tool boundary value problems resonance

Alaa Almansour 1 ; Paul Eloe 1

1 Department of Mathematics University of Dayton Dayton, OH 45469-2316, U.S.A. 
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Alaa Almansour; Paul Eloe. Fixed points and solutions of
 boundary value problems at resonance. Annales Polonici Mathematici, Tome 115 (2015) no. 3, pp. 263-274. doi: 10.4064/ap115-3-5

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