Caraballo, Tomás; Liu, Kai Exponential stability of mild solutions of stochastic partial differential equations with delays. (English) Zbl 0943.60050 Stochastic Anal. Appl. 17, No. 5, 743-763 (1999). Sufficient conditions for exponential stability in the \(p\)th mean are given for mild solutions of a semilinear stochastic partial differential equation with variable delays. Reviewer: T.C.Gard (Athens/Georgia) Cited in 1 ReviewCited in 50 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) Keywords:exponential stability; stochastic partial differential equations; time delays PDF BibTeX XML Cite \textit{T. Caraballo} and \textit{K. Liu}, Stochastic Anal. Appl. 17, No. 5, 743--763 (1999; Zbl 0943.60050) Full Text: DOI References: [1] Caraballo T., Tesis Doctoral (1988) [2] Caraballo T., Asymptotic Exponential Stability of Stochastic Partial Differential Equations with Delay 33 pp 27– (1990) · Zbl 0723.60074 [3] DOI: 10.1080/07362999308809330 · Zbl 0790.60054 · doi:10.1080/07362999308809330 [4] DOI: 10.1080/07362999408809370 · Zbl 0808.93069 · doi:10.1080/07362999408809370 [5] DOI: 10.1016/0022-247X(82)90110-X · Zbl 0496.60059 · doi:10.1016/0022-247X(82)90110-X [6] DOI: 10.1016/0022-247X(81)90031-7 · Zbl 0452.60072 · doi:10.1016/0022-247X(81)90031-7 [7] DOI: 10.1017/CBO9780511666223 · doi:10.1017/CBO9780511666223 [8] DOI: 10.1080/07362999208809260 · Zbl 0758.60049 · doi:10.1080/07362999208809260 [9] El’sgol’ts L.E., Introduction to the Theory and Applications of Differential Equations with Deviating Arguments (1973) [10] DOI: 10.1016/0022-247X(78)90211-1 · Zbl 0385.93051 · doi:10.1016/0022-247X(78)90211-1 [11] DOI: 10.1016/0022-247X(82)90041-5 · Zbl 0497.93055 · doi:10.1016/0022-247X(82)90041-5 [12] Krasovski N.N., Stability of motions (1963) [13] DOI: 10.1016/0022-0396(68)90028-4 · Zbl 0169.11601 · doi:10.1016/0022-0396(68)90028-4 [14] Ladde G.S., Oscillation theory of differential equations with deviating arguments (1987) · Zbl 0832.34071 [15] DOI: 10.1093/qmath/42.1.77 · Zbl 0719.60062 · doi:10.1093/qmath/42.1.77 [16] Real J., Stochastics 8 pp 81– (1982) · Zbl 0511.60056 · doi:10.1080/17442508208833230 [17] Zabczyk, J. 1979.On stability of infinite dimensional stochastic systems, Probability Theory, Edited by: Ciesislki, Z. Vol. 5, 273–281. New York: Banach Center Publications. [18] Zabczyk J., Linear stochastic systems in Hilbert spaces: structural properties and limit behaviour 24 (1985) · Zbl 0573.93076 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.