Lyapunov type integral inequalities for certain differential equations.

Pachpatte, B.G.

Displaying similar documents to “Lyapunov type integral inequalities for certain differential equations.”

Improvements of some integral inequalities of H. Gauchman involving Taylor's remainder.

Akkouchi, Mohamed (2003)

Divulgaciones Matemáticas

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Some quadratic integral inequalities of Opial type

Małgorzata Kuchta (1996)

Annales Polonici Mathematici

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We derive and investigate integral inequalities of Opial type: $\int_{I} s | h h ̇ | d t \leq \int_{I} r h ̇ ² d t$ , 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....