ANZIAM J.
44 (2003), 393-407
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Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions
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Daniel Franco
Departamento de Matemática Aplicada I
ETSI Industriales
UNED
Apartado de Correos 60149
28080 Madrid
Spain
dfranco@ind.uned.es
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Rodrigo L. Pouso
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 linear problem,
giving a complete characterisation of resonance
for it.
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