On the differential equation \(y''+p(t)|{}y' |\) sgn \(y + q(t)y=0\) (Q1199194)
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scientific article; zbMATH DE number 93613
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the differential equation \(y''+p(t)|{}y' |\) sgn \(y + q(t)y=0\) |
scientific article; zbMATH DE number 93613 |
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On the differential equation \(y''+p(t)|{}y' |\) sgn \(y + q(t)y=0\) (English)
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16 January 1993
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Separation and comparison theorems of the Sturm-Picone type are obtained for the zeros of solutions of the equation \((ry')'+p| y'|\text{sgn} y+qy=0\), where \(p\), \(q\), \(r'\) are piecewise continuous functions in an interval, and \(r>0\). As applications, sharp inequalities are proved of the type discovered by de la Vallée Poussin, Opial, and by \textit{J. H. E. Cohn} [Q. J. Math., Oxf. II. Ser. 39, No. 154, 173-174 (1988; Zbl 0668.34036)].
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separation and comparison theorems of the Sturm-Picone type
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inequalities
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