LYAPUNOV STABILITY FOR MEASURE DIFFERENTIAL EQUATIONS

被引：1

作者：

D'Apice, C. ^{[1
]}

Manzo, R. ^{[2
]}

Piccoli, B. ^{[3
]}

Vespri, V. ^{[4
]}

机构：

[1] Univ Salerno, Dept Business Sci Management Innovat Syst, Salerno, Italy

[2] Univ Salerno, Dept Polit & Commun Sci, Salerno, Italy

[3] Rutgers Univ Camden, Dept Math Sci, Camden, NJ 08102 USA

[4] Univ Florence, Dept Mat, Florence, Italy

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2024年 / 14卷 / 04期

关键词：

Measure differential equations; Lyapunov stability; asymptotic stability; doi; WASSERSTEIN SPACES;

D O I：

10.3934/mcrf.2024028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, the concept of measure differential equation was introduced in [17]. Such a concept allows for deterministic modeling of uncertainty, finite-speed diffusion, concentration, and other phenomena. Moreover, it represents a natural generalization of ordinary differential equations to measures. In this paper, we deal with the stability of fixed points for measure differential equations. In particular, we discuss two concepts related to classical Lyapunov stability in terms of measure support and first moment. The two concepts are not comparable, but the latter implies the former if the measure differential equation is defined by an ordinary one. Finally, we provide results concerning Lyapunov functions.

引用

页码：1391 / 1407

页数：17

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