GLOBAL EXISTENCE AND STABILITY OF SOME SEMILINEAR PROBLEMS

M. Kirane and N.-E. Tatar

Address. Mokhtar KIRANE, Universit\'e de Picardie Jules Vernes, Faculte de Mathematiques et d'Informatique, 33, rue Saint Leu, 80039 Amiens Cedex 1, FRANCE

Nasser-Eddine TATAR, Institut de Mathematiques, Universite Badji Mokhtar, B.P.12, El-Hadjar, 23000 Annaba, ALGERIE

E-mail: Mokhtar.Kirane@u-picardie.fr

Abstract. We prove global existence and stability results for a semilinear parabolic equation, a semilinear functional equation and a semilinear integral equation using an inequality which may be viewed as a nonlinear singular version of the well known Gronwall and Bihari inequalities.

AMSclassification. 34D05, 35B35, 35K55

Keywords. Semilinear parabolic equation, functional differential equation, integrodifferential equation, integral equation fractional evolution equation, global existence,\linebreak stability, variation of parameters