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Difference Equations and Inequalities: Theory, Methods, and Applications
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In this paper, the authors consider linear initial value problems, Sturm-Liouville problems and related inequalities in several independent variables, including difference inequalities and boundary value problems for linear systems and nonlinear systems.Abstract:
Preliminaries linear initial value problems miscellaneous difference equations difference inequalities qualitative properties of solutions of difference systems qualitative properties of solutions of higher order difference equations qualitative properties of solutions of neutral difference equations boundary value problems for linear systems boundary value problems for nonlinear systems miscellaneous properties of solutions of higher order linear difference equations boundary value problems for higher order difference equations Sturm-Liouville problems and related inequalities difference inequalities in several independent variables.read more
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Input-to-state stability for discrete-time nonlinear systems
Zhong-Ping Jiang,Yuan Wang +1 more
TL;DR: The input-to-state stability property and small-gain theorems are introduced as the cornerstone of new stability criteria for discrete-time nonlinear systems.
Book
Half-linear differential equations
Ondřej Došlý,Pavel Řehák +1 more
TL;DR: The Handbook of Differential Equations (A.Canada, P. Drabek, A. Fonda, the authors ) provides a survey of qualitative analysis of half-linear differential equations.
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A converse Lyapunov theorem for discrete-time systems with disturbances
Zhong-Ping Jiang,Yuan Wang +1 more
TL;DR: It is shown that a smooth Lyapunov function exists for a family of time-varying discrete systems if these systems are robustly globally asymptotically stable.
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Aggregative games and best-reply potentials
TL;DR: In this article, the authors introduce quasi-aggregative games and establish conditions under which such games admit a best-reply potential, which implies existence of a pure strategy Nash equilibrium without any convexity or quasi-concavity assumptions.
Journal ArticleDOI
Existence of periodic and subharmonic solutions for second-order superlinear difference equations
Zhiming Guo,Jianshe Yu +1 more
TL;DR: In this article, the existence and multiplicity results of periodic and subharmonic solutions for difference equations were studied by critical point theory, and some new results were obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.