References
[ABR] Arendt, W., C.J.K. Batty and D.W. Robinson,Positive semigroups generated by elliptic operators on Lie groups, J. Operator Theory, to appear.
[ACK] Arendt, W., P. Chernoff and T. Kato,A generalization of dissipativity and positive semigroups, J. Operator Theory8 (1982), 167–180.
[Ba] Batty, C.J.K.,Derivations on the line and flows along orbits, Pacific J. Math.126 (1987), 209–225.
[CT] Clément, Ph., and C.A. Timmermans,On C 0-semigroups generated by differential operators satisfying Ventcel's boundary conditions, Indag. Math.89 (1986), 379–387.
[De] DeLaubenfels, R.,Well-behaved derivations on C[0,1], Pacific J. Math.115, (1984), 73–80.
[Do] Dorroh, J.R.,Contraction semigroups in a function space, Pacific J. Math.19 (1966), 35–38.
[Fe1] Feller, W.,The parabolic differential equations and the associated semigroups of operators, Ann. Math.55 (1952), 468–519.
[Fe2] Feller, W.,The general diffusion operator and positivity preserving semigroups in one dimension, Ann. Math.10 (1954), 417–463.
[Fe3] Feller, W.,On second order differential operators, Ann. Math.61 (1955), 90–105.
[Fe4] Feller, W.,Generalized second order differential operators and their lateral conditions, Illinois J. Math.1 (1957), 459–504.
[Go] Goldstein, J.A., “Semigroups of Linear Operators and Applications,” Oxford University Press, 1985.
[GL1] Goldstein, J.A., and C.Y. Lin,Highly degenerate parabolic bounary value problems, Differential and Integral Equations2 (1989), 216–227.
[GL2] Goldstein, J.A., and C.Y. Lin,Singular nonlinear parabolic boundary value problems in one space dimension, J. Differential Equations68 (1987), 429–443.
[GL] Gustafson, K., and G. Lumer,Multiplicative perturbation of semigroup generators, Pacific J. Math.41 (1972), 731–742.
[Hi] Hille, E.,The abstract Cauchy problem and Cauchy's problem for parabolic differential equations, J. d'Analyse Math.3 (1954), 81–196.
[IK] Itô K., and H.P. McKean, “Diffusion Processes and Their Sample Path”, Springer-Verlag, Berlin-Heidelberg-New York, 1965.
[Ma] Mandl, P., “Analytical Treatment of One-Dimensional Markov Processes”, Springer-Verlag, Berlin-Heidelberg-New York, 1968.
[MO] Miyajima, S., and N. Okazawa,Generators of positive C 0-semigroups, Pacific J. Math.125 (1986), 161–175.
[MS] Munteanu, M., and M. Schwarz,A characterization of generators of positive translation semigroups, Semigroup Forum38 (1989), 223–231.
[Na]] Nagel, R. (ed.), “One-Parameter Semigroups of Positive Operators,” Lect. Notes Math.1184, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1986.
[St] Steinmüller, E.,Differentialoperatoren zweiter Ordnung als Generatoren von Operatorhalbgruppen auf C[0,1], Diplomarbeit, Tübingen, 1982.
[Ta1] Taira, K.,Semigroups and boundary value problems, Duke Math. J.49 (1982), 287–320.
[Ta2] Taira, K.,Semigroups and boundary value problems II, Proc. Japan Acad.58A (1982), 277–280.
[Yo] Yosida, K., “Functional Analysis,” Springer-Verlag, Berlin-Heidelberg-New York, 1968.
Author information
Authors and Affiliations
Additional information
Communicated by Jerome A. Goldstein
Rights and permissions
About this article
Cite this article
Ulmet, M.G. Boundary conditions for one-dimensional positive semigroups. Semigroup Forum 45, 92–119 (1992). https://doi.org/10.1007/BF03025753
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF03025753