Book Review: Qualitative theory of differential equations.

Differential Equations ( Qualitative Differential Equations ) Qualitative Constraints Qualitative Simulation

ion Perturbation Statistical Analysis (e.g. Regression Methods) Dynamic System System Behavior Quantitative System Behavior Qualitative System Behavior (Qualitative States) (Numerical Data) Inductive Learning (e.g. GENMODEL) Figure 1. Qualitative reasoning is an abstraction of mathematical reasoning with di erential equations and continuously di erentiable functions. and an initial state, we ca...

Eighth Colloquium on the Qualitative Theory of Differential Equations

A question which has been open in the theory of stochastic equations with delay for around 25 years is: what conditions on the coefficients of a linear stochastic functional differential equations characterise the mean square stability of the solution? In this talk, a simple proof is supplied for a one-dimensional linear Volterra equation. The arguments extend to equations with finite memory or...

A First Course in the Qualitative Theory of Differential Equations

Qualitative Theory of Half-linear Second Order Differential Equations

Some recent results concerning properties of solutions of the half-linear second order differential equation (∗) (r(t)Φ(x′))′ + c(t)Φ(x) = 0, Φ(x) := |x|p−2x, p > 1, are presented. A particular attention is paid to the oscillation theory of (∗). Related problems are also discussed.

Theory of hybrid differential equations on time scales

‎In this paper‎, ‎we develop the theory of hybrid differential‎ ‎equations on time scales‎. ‎An existence theorem for hybrid‎ ‎differential equations on time scales is given under Lipschitz ‎conditions‎. ‎Some fundamental fractional differential inequalities‎ ‎are also established which are utilized to prove the existence of‎ ‎extremal solutions‎. ‎Necessary tools are considered and the‎ ‎compa...