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Dynamic Picone's identity and its applications |
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| Authors: | Nguyen Du Vi Nhan Dinh Thanh Duc Vu Kim Tuan Tran Dinh Phung |
| Affiliation: | 1. Department of Mathematics, Quy Nhon University, Binh Dinh, Viet Nam;2. Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA |
| Abstract: | We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory. |
| Keywords: | Dynamic system Picone's identity Wirtinger's inequality Hardy's inequality Reid's roundabout theorem Sturm's theory |
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