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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
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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