Boundary value problems for functional differential equations with 𝐿² initial functions

Reddien, G. W.; Webb, G. F.

doi:10.1090/S0002-9947-1976-0598112-6

Boundary value problems for functional differential equations with $L^{2}$ initial functions
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by G. W. Reddien and G. F. Webb

Trans. Amer. Math. Soc. 223 (1976), 305-321

DOI: https://doi.org/10.1090/S0002-9947-1976-0598112-6

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Abstract:

Existence results are given for boundary value problems for vector systems of functional differential equations with ${L^2}$ initial functions. The proofs are essentially constructive and lead to computational methods in important cases.

References

K. de Nevers and K. Schmitt, An application of the shooting method to boundary value problems for second order delay equations, J. Math. Anal. Appl. 36 (1971), 588–597. MR 298166, DOI 10.1016/0022-247X(71)90041-2
Robert Fennell and Paul Waltman, A boundary value problem for a system of nonlinear functional differential equations, J. Math. Anal. Appl. 26 (1969), 447–453. MR 237908, DOI 10.1016/0022-247X(69)90167-X
L. J. Grimm and K. Schmitt, Boundary value problems for differential equations with deviating arguments, Aequationes Math. 4 (1970), 176–190. MR 262632, DOI 10.1007/BF01817758
Jack K. Hale, Functional differential equations, Analytic theory of differential equations (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1970) Lecture Notes in Math., Vol. 183, Springer, Berlin, 1971, pp. 9–22. MR 0390425
G. W. Reddien and C. C. Travis, Approximation methods for boundary value problems of differential equations with functional arguments, J. Math. Anal. Appl. 46 (1974), 62–74. MR 339506, DOI 10.1016/0022-247X(74)90281-9

Numerical approximation of nonlinear functional differential equations with

initial functions

Paul Waltman and James S. W. Wong, Two point boundary value problems for nonlinear functional differential equations, Trans. Amer. Math. Soc. 164 (1972), 39–54. MR 287126, DOI 10.1090/S0002-9947-1972-0287126-8
G. F. Webb, Autonomous nonlinear functional differential equations and nonlinear semigroups, J. Math. Anal. Appl. 46 (1974), 1–12. MR 348224, DOI 10.1016/0022-247X(74)90277-7
G. F. Webb, Functional differential equations and nonlinear semigroups in $L^{p}$-spaces, J. Differential Equations 20 (1976), no. 1, 71–89. MR 390422, DOI 10.1016/0022-0396(76)90097-8