About monotonic and oscillatory solutions of scalar linear differential equations with measures as coefficients
Abstract
The monotonic and oscillatory solutions of the first order scalar ordinary differential equations are studied. Some essential differences between the classical, Carathéodory and measures-coefficients cases are presented. Next some sufficient conditions for monotonicity or oscillations of all solutions of the equation under consideration are presented. One theorem about differential inequalities is also proved.
References
2. U. Sztaba, Research of solutions of some generalizations of ordinary differential equations, Thesis, Katowice 1978 (in Polish).
3. Z. Wyderka, Some problems of optimal control for linear systems, Thesis, Katowice 1979 (in Polish).
4. Z. Wyderka, Linear differential equations with measures as coefficients and control theory, Časopis Pést. Mat. 14 (1989), 13-27.
5. Z. Wyderka, On stability and stabilization of linear systems with measures as coefficients, Fasc. Math. 18 (1988), 81-98.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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