References
Benilan, Ph.: Equations d'évolution dans un espace de Banach quelconque et applications. Thesis, Orsay, 1972
Bittner, L.: Die elementaren Differential- und Integralungleichungen mit einem allgemeinen Ungleichungsbegriff. Math. Nachr.38, 1–17 (1968)
Bony, J.M.: Principe du maximum, inégalité de Harnack et unicité du probléme de Cauchy pour les opérateurs elliptiques dégénérés. Ann. Inst. Fourier Grenoble19, 277–304 (1969)
Brezis, H.: On a characterization of flow-invariant sets. Commun. Pure Appl. Math.23, 261–263 (1970)
Brezis, H., Pazy, A.: Accretive sets and differential equations in Banach spaces. Israel Jnl. Math.9, 367–383 (1970)
Browder, F.E.: Nonlinear equations of evolution and nonlinear accretive operators in Banach spaces. Bull. MS73, 868–874 (1967)
Crandall, M.G.: Differential equations on convex sets. Jnl. Math. Soc. Japan,22, 443–455 (1970)
Crandall, M.G.: Semigroups of nonlinear transformations in Banach spaces, contribution to nonlinear functional analysis. 157–179. New York: Acad. Press Inc. 1971
Crandall, M.G.: A generalization of Peano's existence theorem and flow invariance. Proc. AMS37, 151–155 (1972)
Crandall, M.G., Liggett, T.M.: Generation of semi-groups of nonlinear transformations on general Banach spaces. Am. Jnl. Math. XCIII, 265–298 (1971)
Crandall, M.G., Pazy, A.: Nonlinear evolution equations in Banach spaces. Israel Jnl. Math.11, 57–94 (1972)
Hartman, P.: On invariant sets and on a theorem of Wazewski. Proceedings Amer. Math. Soc.32, 511–520 (1972)
Hill, C.D.: A sharp maximum principle for degenerate elliptic-parabolic equations. Ind. Univ. Math. Jnl.20, 213–229 (1970)
Kato, T.: Nonlinear semigroups and evolution equations. J. Mach. Soc. Japan19, 508–520 (1967)
Kato, T.: Accretive operators and nonlinear evolution equations in Banach spaces. Proc. Symp. Pure Math. AMS18 (1), 138–161 (1970)
Lakshmikantham, V.: Upper and lower bounds of the norm of solutions of differential equations. Proc. AMS13, 615–616 (1962)
Lakshmikantham, V.: Notes on a variety of problems of differential systems. Arch. Rat. Mech. and Anal.19, 119–126 (1962)
Lakshmikantham, V., Ladde, G.S.: On flow-invariant sets. Technical Report No. 28, Univ. of Rhode Island, 1972
Martin, R.H., Jr.: A global existence theorem for autonomous differential equations in a Banach space. Proc. AMS26, 307–314 (1970)
Martin, R.H., Jr.: Differential equations on closed subsets of a Banach space. Jnl. Math. Soc. Japan22, 411–429 (1970)
Martin, R.H., Jr.: The logarithmic derivative and equations of evolution in a Banach space. Jnl. Math. Soc. Japan22, 411–429 (1970)
McShane, E.J.: On the uniqueness of solutions to differential equations. Bull. AMS45, 755–757 (1939)
Nagumo, M.: Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen. Proc. Phys. Math. Soc. Japan24, 551–559 (1942)
Redheffer, R.M.: Bemerkungen über Differentialungleichungen bei abzählbaren Ausnahmemengen. Num. Math.9, 437–445 (1967)
Redheffer, R.M.: Gewöhnliche Differentialungleichungen mit quasimonotonen Funktionen in normierten linearen Räumen. Arch. Rational Mech. Anal.52, 121–133 (1973)
Redheffer, R.M.: The theorems of Bony and Brezis on flow-invariant sets. Amer. Math. Monthly79, 740–747 (1972)
Redheffer, R. M., Walter, W.: Flow-invariant sets and differential inequalities in normed spaces. (To appear)
Tapia, R.A.: A characterization of inner product spaces. Proc. Am. Math. Soc.41, 569–574 (1973)
Volkmann, P.: Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen. Math. Zeitschr.127, 157–164 (1972)
Volkmann, P.: Über die Invarianz konvexer Mengen und Differentialungleichungen in normierten Räumen. Math. Annalen203, 201–210 (1973)
Walter, W.: Differential and Integral Inequalities. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 55. Berlin-Heidelberg-New York: Springer 1970
Walter, W.: Gewöhnliche Differential-Ungleichungen im Banachraum. Arch. Math.20, 36–47 (1969)
Walter, W.: Ordinary differential inequalities in ordered Banach spaces. J. Differential Equations9, 253–261 (1971)
Walter, W.: Some new aspects of the line method for parabolic differential equations. Conference on the theory of ordinary and partial differential equations, Dundee 1972. Lecture Notes in Mathematics No. 280. Berlin-Heidelberg-New York: Springer 1972
Yorke, J.A.: Differential inequalities and non-Lipschitz scalar functions. Math. Systems Theory4, 140–153 (1970)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Redheffer, R., Walter, W. A differential inequality for the distance function in normed linear spaces. Math. Ann. 211, 299–314 (1974). https://doi.org/10.1007/BF01418227
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01418227