zbMATH — the first resource for mathematics

Nonlinear Volterra equations with infinite delay. (English) Zbl 0382.45003

45D05 Volterra integral equations
45G10 Other nonlinear integral equations
45M10 Stability theory for integral equations
45L05 Theoretical approximation of solutions to integral equations
Full Text: DOI EuDML
[1] Brewer, D. W.: A Nonlinear Semigroup for a Functional Differential Equation. Dissertation, University of Wisconsin. 1975.
[2] Brezis, H., andA. Pazy: Convergence and approximation of semigroups of nonlinear operators in Banach spaces. J. Funct. Anal.9, 63-64 (1972). · Zbl 0231.47036
[3] Browder, F.: Nonlinear equations of evolution. Ann. Math.80, 485-523 (1964). · Zbl 0127.33602
[4] Crandall, M., andT. Liggett: Generation of semigroups of nonlinear transformations on general Banach spaces. Amer. J. Math.93, 265-298 (1971). · Zbl 0226.47038
[5] Crandall, M., T. Liggett, andA. Pazy: Nonlinear evolution equations in Banach spaces. Israel J. Math.11, 57-94 (1972). · Zbl 0249.34049
[6] Dyson, J., andR. Villella Bressan: Functional differential equations and nonlinear evolution operators. Edinburgh J. Math. (To appear.)
[7] Fitzgibbon, W.: Stability for abstract nonlinear Volterra equations involving finite delay. J. Math. Anal. Appl.60, 429-434 (1977).
[8] Flaschka, H., andM. Leitman: On semigroups of nonlinear operators and the solution of the functional differential equationx(t)=F(x t ). J. Math. Anal. Appl.49, 649-658 (1975). · Zbl 0321.47046
[9] Goldstein, J.: Abstract evolution equations. Trans. Amer. Math. Soc.141, 159-185 (1969). · Zbl 0181.42602
[10] Hale, J.: Functional Differential Equations. New York: Springer. 1971. · Zbl 0222.34003
[11] Laksmikantham, V., andS. Leela: Differential and Integral Inequalities, Vol. II. New York: Academic Press. 1972.
[12] Saaty, T.: Modern Nonlinear Equations. New York: McGraw Hill. 1972. · Zbl 0148.28202
[13] Travis, C., andG. Webb: Existence and stability for partial functional differential equations. Trans. Amer. Math. Soc.200, 395-418 (1974). · Zbl 0299.35085
[14] Webb, G.: Autononomous nonlinear functional differential equations. J. Math. Anal. Appl.46, 1-12 (1974). · Zbl 0277.34070
[15] Webb, G.: Asymptotic stability for abstract nonlinear functional differential equations. Proc. Amer. Math. Soc. (To appear.) · Zbl 0324.34079
[16] Webb, G.: Functional differential equations and nonlinear semigroups inL p -spaces. J. Diff. Equations. (To appear.)
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.