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Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions

Published online by Cambridge University Press:  17 February 2009

Daniel Franco  and
Rodrigo L. Pouso
Daniel Franco
Affiliation:
Departamento de Matemática Aplicada 1, ETSI Industriales, UNED, Apartado de Correos 60149, 28080 Madrid, Spain; e-mail: [email protected].
Rodrigo L. Pouso
Affiliation:
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Sur s/n, 15782 Santiago de Compostela, Spain.
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Abstract

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In this work we shall study the existence of extremal solutions for an impulsive problem with functional-boundary conditions and weak regularity assumptions, not only on the right-hand side of the equation and on the functions that define the boundary conditions, but also on the impulse functions, which will be required to be nondecreasing, but not continuous as well, as is customary in the literature.

Moreover, in order to prove one of our results we shall study a general impulsive linearproblem, giving a complete characterisation of resonance for it.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 3 , January 2003 , pp. 393 - 407
Copyright
Copyright © Australian Mathematical Society 2003

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