Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales

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• 作者：Ravi P. Agarwal ; Erbil Çetin…
• 关键词：Time scale ; Lyapunov inequality ; Forced ; Mixed nonlinear ; Sub ; linear ; Super ; linear
• 刊名：Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：1
• 页码：231-246
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Milan
• ISSN：1579-1505
• 卷排序：111

文摘

In this paper, we present some new Hartman and Lyapunov inequalities for second-order forced dynamic equations on time scales \({\mathbb T}\) with mixed nonlinearities: $$\begin{aligned} x^{\Delta \Delta }(t)+\sum _{k=1}^nq_k(t)|x^{\sigma }(t)|^{\alpha _k-1}x^{\sigma }(t)=f(t);\quad t\in [t_0,\infty )_{\mathbb T}, \end{aligned}$$where the nonlinearities satisfy $$\begin{aligned} 0<\alpha _1<\cdots <\alpha _m<1<\alpha _{m+1}<\cdots <\alpha _n<2. \end{aligned}$$No sign restrictions are imposed on the potentials \(q_k\), \(k=1,2,\ldots ,n\), and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.KeywordsTime scaleLyapunov inequalityForcedMixed nonlinearSub-linearSuper-linearMathematics Subject Classification34C10References1.Agarwal, R.P., Özbekler, A.: Disconjugacy via Lyapunov and Vallée–Poussin type inequalities for forced differential equations. Appl. Math. 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Comput. 215, 3884–3890 (2010)MathSciNetMATHGoogle ScholarCopyright information© Springer-Verlag Italia 2016Authors and AffiliationsRavi P. Agarwal1Erbil Çetin12Abdullah Özbekler13Email author1.Department of MathematicsTexas A&M University-KingsvilleKingsvilleUSA2.Department of MathematicsEge UniversityBornovaTurkey3.Department of MathematicsAtilim UniversityIncekTurkey About this article CrossMark Publisher Name Springer Milan Print ISSN 1578-7303 Online ISSN 1579-1505 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; background-color: #f2f2f2; } .buybox__header .buybox__login { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; 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