Conditions For Oscillation Of Several Classes Of Impulsive Parabolic Differential Equations With Delays

In this paper, we consider the oscillation of several classes ofimpulsive parabolic differential equations with delays. In chapter 1, firstly,Some sufficient conditions of first order impulsive differential inequalities whichdon't have eventually positive solutions ( or eventually negative solutions ) areobtained. Then, the oscillation problems are changed into the problems of firstorder impulsive differential inequalities which don't have eventually positivesolutions ( or eventually negative solutions ) by using averaging technique. Fi-nally, some sufficient conditions for oscillation of impulsive parabolic di?erentialequations are obtained under the homogeneous Neumann boundary conditionby using averaging technique and inequality skills. In chapter 2, the oscillationof solutions of a class of nonlinear impulsive parabolic differential equations withseveral delays is discussed. Some sufficient conditions of impulsive differentialinequalities which don't have eventually positive solutions ( or eventuallynegative solutions ) are obtained by using analyzing technique. Then, theoscillation problems are changed into the problems of impulsive differentialinequalities which don't have eventually positive solutions ( or eventuallynegative solutions ) by using averaging technique. Some sufficient conditionsfor oscillation are obtained under the homogeneous Neumann boundarycondition. In chapter 3, the oscillation of solutions of a class of nonlinearimpulsive parabolic differential systems with several delays is discussed.Some sufficient conditions for oscillation are obtained under the homogeneousNeumann boundary condition by using averaging technique and inequality skills.