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Subexponential growth rates in functional differential equations
1.  Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland 
2.  School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9,, Ireland 
References:
[1] 
J. A. D. Appleby, M. J. McCarthy and A. Rodkina, Growth rates of delaydifferential equations and uniform Euler schemes, Difference equations and applications, (eds. M. Bohner et al.), UǧurBahçeşehir Univ. Publ. Co., Istanbul, (2009), 117124. Google Scholar 
[2] 
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, 27, Cambridge University Press, Cambridge, 1987. Google Scholar 
[3] 
J. R. Graef, Oscillation, nonoscillation, and growth of solutions of nonlinear functional differential equations of arbitrary order, J. Math. Anal. Appl., 60 (1977), 398409. Google Scholar 
[4] 
G. Gripenberg, S.O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics, 34, Cambridge University Press, Cambridge, 1990. Google Scholar 
[5] 
P. Hartman and A. Wintner, Asymptotic integration of ordinary nonlinear differential equations, Amer. J. Math., 77 (1955), 692724. Google Scholar 
[6] 
P. Hartman, Ordinary differential equations, $2^{nd}$ edition, SIAM, Philadelphia, 2002. Google Scholar 
[7] 
T. Kusano and H. Onose, Oscillatory and asymptotic behavior of sublinear retarded differential equations Hiroshima Math. J., 4 (1974), 343355. Google Scholar 
[8] 
M. Pituk, The HartmanWintner Theorem for Functional Differential Equations, J. Differential Equations, 155 (1), (1999), 116. Google Scholar 
show all references
References:
[1] 
J. A. D. Appleby, M. J. McCarthy and A. Rodkina, Growth rates of delaydifferential equations and uniform Euler schemes, Difference equations and applications, (eds. M. Bohner et al.), UǧurBahçeşehir Univ. Publ. Co., Istanbul, (2009), 117124. Google Scholar 
[2] 
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, 27, Cambridge University Press, Cambridge, 1987. Google Scholar 
[3] 
J. R. Graef, Oscillation, nonoscillation, and growth of solutions of nonlinear functional differential equations of arbitrary order, J. Math. Anal. Appl., 60 (1977), 398409. Google Scholar 
[4] 
G. Gripenberg, S.O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics, 34, Cambridge University Press, Cambridge, 1990. Google Scholar 
[5] 
P. Hartman and A. Wintner, Asymptotic integration of ordinary nonlinear differential equations, Amer. J. Math., 77 (1955), 692724. Google Scholar 
[6] 
P. Hartman, Ordinary differential equations, $2^{nd}$ edition, SIAM, Philadelphia, 2002. Google Scholar 
[7] 
T. Kusano and H. Onose, Oscillatory and asymptotic behavior of sublinear retarded differential equations Hiroshima Math. J., 4 (1974), 343355. Google Scholar 
[8] 
M. Pituk, The HartmanWintner Theorem for Functional Differential Equations, J. Differential Equations, 155 (1), (1999), 116. Google Scholar 
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