Some quadratic integral inequalities of Opial type
Małgorzata Kuchta
Annales Polonici Mathematici, Tome 63 (1996), p. 103-113 / Harvested from The Polish Digital Mathematics Library
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We derive and investigate integral inequalities of Opial type: ∫Is|hḣ|dt≤∫Irḣ²dt, where h ∈ H, I = (α,β) is any interval on the real line, H is a class of absolutely continuous functions h satisfying h(α) = 0 or h(β) = 0. Our method is a generalization of the method of [3]-[5]. Given the function r we determine the class of functions s for which quadratic integral inequalities of Opial type hold. Such classes have hitherto been described as the classes of solutions of a certain differential equation. In this paper a wider class of functions s is given which is the set of solutions of a certain differential inequality. This class is determined directly and some new inequalities are found.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:262697 
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Małgorzata Kuchta. Some quadratic integral inequalities of Opial type. Annales Polonici Mathematici, Tome 63 (1996) pp. 103-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z2p103bwm/

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