Journal of Applied Mathematics and Stochastic Analysis 
Volume 6 (1993), Issue 3, Pages 247-260
doi:10.1155/S1048953393000206

Impulsive nonlocal nonlinear parabolic differential problems

Ludwik Byszewski

 Cracow University of Technology, Institute of Mathematics, Cracow 31-155, Poland
Received 1 March 1993; Revised 1 June 1993

Abstract

The aim of the paper is to prove a theorem about a weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities. A weak maximum principle for an impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities and an uniqueness criterion for the existence of the classical solution of an impulsive nonlocal nonlinear parabolic differential problem are obtained as a consequence of the theorem about the weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities.