Wirtinger Inequality and Nonlinear Differential Systems
نویسنده
چکیده
Picone identity for a class of nonlinear differential equations is established and various qualitative results (such as Wirtinger-type inequality and the existence of zeros of first components of solutions) are obtained with the help of this new formula.
منابع مشابه
Picone’s Identity for a System of First-order Nonlinear Partial Differential Equations
We established a Picone identity for systems of nonlinear partial differential equations of first-order. With the help of this formula, we obtain qualitative results such as an integral inequality of Wirtinger type and the existence of zeros for the first components of solutions in a given bounded domain.
متن کاملImproved Results on Stability of Time-delay Systems using Wirtinger-based Inequality
This paper concerns with the problem of delay-dependent stability analysis of time-delay systems. By help of Wirtinger based inequality which gives very close estimating bound of Jensen’s inequality, an extended inequality is proposed. Using the new inequality and tuning parameters, a generalized criterion for stability of time-delay systems is established. Two numerical examples are given to d...
متن کاملFrom Toeplitz Eigenvalues through Green’s Kernels to Higher-Order Wirtinger-Sobolev Inequalities
The paper is concerned with a sequence of constants which appear in several problems. These problems include the minimal eigenvalue of certain positive definite Toeplitz matrices, the minimal eigenvalue of some higher-order ordinary differential operators, the norm of the Green kernels of these operators, the best constant in a Wirtinger-Sobolev inequality, and the conditioning of a special lea...
متن کاملA sharp weighted Wirtinger inequality and some related functional spaces
We consider the generalized Wirtinger inequality
متن کاملH∞ analysis and switching control for uncertain discrete switched time-delay systems by discrete Wirtinger inequality
*Correspondence: [email protected] Department of Marine Engineering, National Kaohsiung Marine University, Kaohsiung, 811, Taiwan, R.O.C. Abstract In this paper, the H∞ performance analysis and switching control of uncertain discrete switched systems with time delay and linear fractional perturbations are considered via a switching signal design. Lyapunov-Krasovskii type functional and di...
متن کامل