Lyapunov inequalities for dynamic equations via new Opial type inequalities
نویسندگان
چکیده
منابع مشابه
Lyapunov-type Inequalities for Differential Equations
Let us consider the linear boundary value problem u′′(x) + a(x)u(x) = 0, x ∈ (0, L), u′(0) = u′(L) = 0, (0.1) where a ∈ Λ0 and Λ0 is defined by Λ0 = {a ∈ L∞(0, L) \ {0} : Z L 0 a(x) dx ≥ 0, (0.1) has nontrivial solutions}. Classical Lyapunov inequality states that Z L 0 a(x) dx > 4/L for any function a ∈ Λ0, where a(x) = max{a(x), 0}. The constant 4/L is optimal. Let us note that Lyapunov inequ...
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* Correspondence: chjzhao@163. com Department of Mathematics, China Jiliang University, Hangzhou 310018, PR China Full list of author information is available at the end of the article Abstract In the present paper we establish some new Opial-type inequalities involving higherorder partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality and also ...
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In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality. As application, we prove the uniqueness of the solution of initial value problem involving higher order partial differential equation. Mathematics subject classification (2010): 26D15.
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ژورنال
عنوان ژورنال: Hacettepe Journal of Mathematics and Statistics
سال: 2018
ISSN: 1303-5010
DOI: 10.15672/hjms.2018.631