Appleby, John A. D. Mean square characterisation of a stochastic Volterra integrodifferential equation with delay. (English) Zbl 1482.34194 Int. J. Dyn. Syst. Differ. Equ. 11, No. 3-4, 194-226 (2021). MSC: 34K50 45R05 45M05 PDFBibTeX XMLCite \textit{J. A. D. Appleby}, Int. J. Dyn. Syst. Differ. Equ. 11, No. 3--4, 194--226 (2021; Zbl 1482.34194) Full Text: DOI
Appleby, John A. D.; Patterson, Denis D. Growth and fluctuation in perturbed nonlinear Volterra equations. (English) Zbl 1508.34095 Appl. Math. Comput. 396, Article ID 125938, 35 p. (2021). MSC: 34K25 34K27 34K50 45D05 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. D. Patterson}, Appl. Math. Comput. 396, Article ID 125938, 35 p. (2021; Zbl 1508.34095) Full Text: DOI arXiv
Appleby, John A. D.; Patterson, Denis D. Blow-up and superexponential growth in superlinear Volterra equations. (English) Zbl 1395.45013 Discrete Contin. Dyn. Syst. 38, No. 8, 3993-4017 (2018). MSC: 45J05 45M05 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. D. Patterson}, Discrete Contin. Dyn. Syst. 38, No. 8, 3993--4017 (2018; Zbl 1395.45013) Full Text: DOI arXiv
Appleby, John A. D.; Patterson, Denis D. Growth rates of sublinear functional and Volterra differential equations. (English) Zbl 1454.34103 SIAM J. Math. Anal. 50, No. 2, 2086-2110 (2018). MSC: 34K25 34K12 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. D. Patterson}, SIAM J. Math. Anal. 50, No. 2, 2086--2110 (2018; Zbl 1454.34103) Full Text: DOI arXiv
Appleby, John A. D.; Patterson, Denis D. Memory dependent growth in sublinear Volterra differential equations. (English) Zbl 1384.45002 J. Integral Equations Appl. 29, No. 4, 531-584 (2017). MSC: 45D05 45G10 45M05 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. D. Patterson}, J. Integral Equations Appl. 29, No. 4, 531--584 (2017; Zbl 1384.45002) Full Text: DOI arXiv Euclid
Appleby, John A. D.; Patterson, Denis D. Large fluctuations and growth rates of linear Volterra summation equations. (English) Zbl 1378.39002 J. Difference Equ. Appl. 23, No. 6, 1047-1080 (2017). Reviewer: Miloš Čanak (Beograd) MSC: 39A06 39A22 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. D. Patterson}, J. Difference Equ. Appl. 23, No. 6, 1047--1080 (2017; Zbl 1378.39002) Full Text: DOI arXiv
Appleby, John A. D.; Patterson, Denis D. Hartman-Wintner growth results for sublinear functional differential equations. (English) Zbl 1357.34116 Electron. J. Differ. Equ. 2017, Paper No. 21, 45 p. (2017). MSC: 34K12 34K25 34K28 45D05 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. D. Patterson}, Electron. J. Differ. Equ. 2017, Paper No. 21, 45 p. (2017; Zbl 1357.34116) Full Text: arXiv Link
Patterson, Denis D.; Appleby, John A. D. Subexponential growth rates in functional differential equations. (English) Zbl 1336.34097 Discrete Contin. Dyn. Syst. 2015, Suppl., 56-65 (2015). MSC: 34K12 34K25 PDFBibTeX XMLCite \textit{D. D. Patterson} and \textit{J. A. D. Appleby}, Discrete Contin. Dyn. Syst. 2015, 56--65 (2015; Zbl 1336.34097) Full Text: DOI arXiv
Appleby, John A. D.; Daniels, John A.; Reynolds, David W. On the Admissibility of Linear Stochastic Volterra Operators. arXiv:1210.6064 Preprint, arXiv:1210.6064 [math.PR] (2012). MSC: 47G10 60H20 45P05 45M05 45A05 45D05 BibTeX Cite \textit{J. A. D. Appleby} et al., ``On the Admissibility of Linear Stochastic Volterra Operators'', Preprint, arXiv:1210.6064 [math.PR] (2012) Full Text: arXiv OA License
Reynolds, David W.; Appleby, John A. D. Decay rates of solutions of linear stochastic Volterra equations. (English) Zbl 1188.45008 Electron. J. Probab. 13, 922-943 (2008). MSC: 45R05 60H20 45M05 45M10 45M20 PDFBibTeX XMLCite \textit{D. W. Reynolds} and \textit{J. A. D. Appleby}, Electron. J. Probab. 13, 922--943 (2008; Zbl 1188.45008) Full Text: DOI EuDML EMIS
Reynolds, David W.; Appleby, John A. D.; Győri, István On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity. (English) Zbl 1164.45001 Note Mat. 27, No. 2, 215-228 (2007). Reviewer: Gustaf Gripenberg (Hut) MSC: 45D05 74D05 45M05 PDFBibTeX XMLCite \textit{D. W. Reynolds} et al., Note Mat. 27, No. 2, 215--228 (2007; Zbl 1164.45001)
Appleby, John A. D.; Devin, Siobhán; Reynolds, David W. Almost sure convergence of solutions of linear stochastic Volterra equations to nonequilibrium limits. (English) Zbl 1154.45012 J. Integral Equations Appl. 19, No. 4, 405-437 (2007). Reviewer: Rainer Buckdahn (Brest) MSC: 45R05 45J05 60H20 45M05 45M10 PDFBibTeX XMLCite \textit{J. A. D. Appleby} et al., J. Integral Equations Appl. 19, No. 4, 405--437 (2007; Zbl 1154.45012) Full Text: DOI
Appleby, John A. D.; Fabrizio, Mauro; Lazzari, Barbara; Reynolds, David W. On exponential asymptotic stability in linear viscoelasticity. (English) Zbl 1114.45003 Math. Models Methods Appl. Sci. 16, No. 10, 1677-1694 (2006). Reviewer: Jacek Banasiak (Durban) MSC: 45N05 45K05 74D05 47D06 45M05 45M10 PDFBibTeX XMLCite \textit{J. A. D. Appleby} et al., Math. Models Methods Appl. Sci. 16, No. 10, 1677--1694 (2006; Zbl 1114.45003) Full Text: DOI
Appleby, J. A. D.; Reynolds, D. W. Subexponential solutions of linear integro-differential equations. (English) Zbl 1069.45007 Ladde, G.S.(ed.) et al., Dynamic systems and applications. Volume 4. Proceedings of the 4th international conference, Morehouse College, Atlanta, GA, USA, May 21–24, 2003. Atlanta, GA: Dynamic Publishers (ISBN 1-890888-00-1/hbk). 488-494 (2004). MSC: 45J05 45M05 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. W. Reynolds}, in: Dynamic systems and applications. Volume 4. Proceedings of the 4th international conference, Morehouse College, Atlanta, GA, USA, May 21--24, 2003. Atlanta, GA: Dynamic Publishers. 488--494 (2004; Zbl 1069.45007)
Appleby, J. A. D.; Győri, I.; Reynolds, D. W. Subexponential solutions of scalar linear integro-differential equations with delay. (English) Zbl 1063.45005 Funct. Differ. Equ. 11, No. 1-2, 11-18 (2004). Reviewer: Gustaf Gripenberg (Hut) MSC: 45J05 45M05 45M10 PDFBibTeX XMLCite \textit{J. A. D. Appleby} et al., Funct. Differ. Equ. 11, No. 1--2, 11--18 (2004; Zbl 1063.45005)
Appleby, John A. D.; Reynolds, David W. On the non-exponential decay to equilibrium of solutions of nonlinear scalar Volterra integro-differential equations. (English) Zbl 1071.45005 Electron. J. Qual. Theory Differ. Equ. 2003, Suppl., Paper No. 3, 14 p. (2003). MSC: 45J05 45G10 45M05 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. W. Reynolds}, Electron. J. Qual. Theory Differ. Equ. 2003, Paper No. 3, 14 p. (2003; Zbl 1071.45005) Full Text: EuDML EMIS
Appleby, John A. D.; Reynolds, David W. Corrigendum: Subexponential solutions of linear integro-differential equations and transient renewal equations. (English) Zbl 1047.45003 Proc. R. Soc. Edinb., Sect. A, Math. 133, No. 6, 1521 (2003). Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 45J05 45M10 45M05 34K25 60K05 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. W. Reynolds}, Proc. R. Soc. Edinb., Sect. A, Math. 133, No. 6, 1521 (2003; Zbl 1047.45003)
Appleby, John A. D.; Reynolds, David W. On the non-exponential convergence of asymptotically stable solutions of linear scalar Volterra integro-differential equations. (English) Zbl 1041.45009 J. Integral Equations Appl. 14, No. 2, 109-118 (2002). MSC: 45J05 45M05 45M10 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. W. Reynolds}, J. Integral Equations Appl. 14, No. 2, 109--118 (2002; Zbl 1041.45009) Full Text: DOI
Appleby, John A. D.; Reynolds, David W. Subexponential solutions of linear integro-differential equations and transient renewal equations. (English) Zbl 1009.45007 Proc. R. Soc. Edinb., Sect. A, Math. 132, No. 3, 521-543 (2002). Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 45J05 45M05 45M10 PDFBibTeX XMLCite \textit{J. A. D. Appleby} and \textit{D. W. Reynolds}, Proc. R. Soc. Edinb., Sect. A, Math. 132, No. 3, 521--543 (2002; Zbl 1009.45007) Full Text: DOI