论文信息 - Ulam stabilities of ordinary differential equations in a Banach space

Ulam stabilities of ordinary differential equations in a Banach space

Let (B;j j ) be a Banach space, A : B ! B be the infinitesimal generator of a C0- semigroup, I := (a;b) or (a;+1( and f 2 C(I B;B). In this paper we present and discuss four types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the following differential equation u 0 (t) = A(u(t)) +f(t;u(t)); t2 I:

Ioan A. Rus | I. Rus

[1] H. Cao,et al. Stability of Functional Equations in Several Variables , 2007 .

[2] Hassan Fathabadi,et al. On Stability Analysis of Nonlinear Systems , 2012 .

[3] Ioan A. Rus,et al. REMARKS ON ULAM STABILITY OF THE OPERATORIAL EQUATIONS , 2009 .

[4] Soon-Mo Jung,et al. Generalized Hyers-Ulam stability of Riccati differential equation , 2008 .

[5] J. Goldstein. Semigroups of Linear Operators and Applications , 1985 .

[6] Ioan A. Rus,et al. ULAM STABILITY OF ORDINARY DIFFERENTIAL EQUATIONS , 2009 .

[7] Aldo Belleni-Morante,et al. A Concise Guide to Semigroups and Evolution Equations , 1994, Series on Advances in Mathematics for Applied Sciences.

[8] Viorel Radu,et al. THE FIXED POINT ALTERNATIVE AND THE STABILITY OF FUNCTIONAL EQUATIONS , 2003 .

[9] Josip Pečarić,et al. Inequalities Involving Functions and Their Integrals and Derivatives , 1991 .

[10] I. I. Vrabie. C[0]-semigroups and applications , 2003 .

[11] V. Barbu. Nonlinear Semigroups and di erential equations in Banach spaces , 1976 .

[12] George Isac,et al. Stability of Functional Equations in Several Variables , 1998 .

[13] P. Gǎvruţa,et al. A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings , 1994 .

[14] Soon-Mo Jung,et al. HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′ = λy , 2004 .