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Existence theorems for equations in normed spaces and boundary value problems for nonlinear vector ordinary differential equations

Published online by Cambridge University Press:  14 November 2011

A. Cañada  and
R. Ortega
A. Cañada
Affiliation:
Departamento de Ecuaciones Funcionales, Universidad de Granada, Granada, Spain
R. Ortega
Affiliation:
Departamento de Ecuaciones Funcionales, Universidad de Granada, Granada, Spain
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Synopsis

The existence of solutions to equations in normed spaces is proved when the nonlinear part of the equation satisfies growth and asymptotic conditions, whether the linear part is invertible or not. For this, we use the coincidence degree theory developed by Mawhin. We apply our abstract results to boundary value problems for nonlinear vector ordinary differential equations. In particular, we consider the Picard boundary value problem at the first eigenvalue and the periodic boundary value problem at resonance. In both cases, the nonlinear term can be of superlinear type. Also, necessary and sufficient conditions of Landesman-Lazer type are obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 98 , Issue 1-2 , 1984 , pp. 1 - 11
Copyright
Copyright © Royal Society of Edinburgh 1984

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