ANZIAM  J.  44 (2003), 393-407
Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions

Daniel Franco
  Departamento de Matemática Aplicada I
  ETSI Industriales
  Apartado de Correos 60149
  28080 Madrid
Rodrigo L. Pouso
  Departamento de Análise Matemática
  Facultade de Matemáticas
  Universidade de Santiago de Compostela
  Campus Sur s/n
  15782 Santiago de Compostela

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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