Abstract
This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included.
Highlights
Impulsive differential equations, that is, differential equations involving impulse effect, appear as a natural description of observed evolution phenomena of several real world problems
Let x t and y t denote the amounts of drug at time t in the gastrointestinal tract and apparent volume of distribution, respectively, and let k1 and k2 be the relevant rate constants
To the best of our knowledge, except one paper 11, all of the investigations have been on differential equations subject to fixed moments of impulse effect
Summary
That is, differential equations involving impulse effect, appear as a natural description of observed evolution phenomena of several real world problems. Let x t and y t denote the amounts of drug at time t in the gastrointestinal tract and apparent volume of distribution, respectively, and let k1 and k2 be the relevant rate constants. Sufficient conditions are obtained for the asymptotic stability of the zero solution of 1.4 and existence of oscillatory solutions of 1.5 It seems that the problem of oscillation of ordinary differential equations with impulses has received attention much later 10. To the best of our knowledge, except one paper 11 , all of the investigations have been on differential equations subject to fixed moments of impulse effect. In 11 , second-order differential equations with random impulses were dealt with, and there are no papers on the oscillation of differential equations with impulses at variable times.
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