Stability and saddle-point property for a linear autonomous functional parabolic equation

Jaroslav Milota

Commentationes Mathematicae Universitatis Carolinae (1986)

  • Volume: 027, Issue: 1, page 87-101
  • ISSN: 0010-2628

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Milota, Jaroslav. "Stability and saddle-point property for a linear autonomous functional parabolic equation." Commentationes Mathematicae Universitatis Carolinae 027.1 (1986): 87-101. <http://eudml.org/doc/17441>.

@article{Milota1986,
author = {Milota, Jaroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {parabolic functional differential equation; infinite delay; sectorial operator; Banach space; fading memory; stability; saddle-point property},
language = {eng},
number = {1},
pages = {87-101},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Stability and saddle-point property for a linear autonomous functional parabolic equation},
url = {http://eudml.org/doc/17441},
volume = {027},
year = {1986},
}

TY - JOUR
AU - Milota, Jaroslav
TI - Stability and saddle-point property for a linear autonomous functional parabolic equation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1986
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 027
IS - 1
SP - 87
EP - 101
LA - eng
KW - parabolic functional differential equation; infinite delay; sectorial operator; Banach space; fading memory; stability; saddle-point property
UR - http://eudml.org/doc/17441
ER -

References

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  1. BLASIO di G., KUNISH K., SINASTRARI E., Stability for abstract linear functional differential equations, preprint, Universität Graz, 1984. (1984) 
  2. BROWDER F. E., On the spectral theory of elliptic differential operators I, Math. Ann. 142 (1961), 22-130. (1961) Zbl0104.07502MR0209909
  3. COLEMAN B. D., MIZEL V. J., Norms and semigroups in the theory of fading memory, Arch. Rat. Mech. Anal. 23 (1966), 87-123. (1966) MR0210343
  4. FITZGIBBON W. E., Nonlinear Volterra equations with infinite delay, Monatsh. Math. 84 (1972), 275-288. (1972) MR0481982
  5. FRIEDMAN A., Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969. (1969) Zbl0224.35002MR0445088
  6. HALE J., Theory of Functional Differential Equations, Appl. Math. Sciences, Vol. 3, Springer - Verlag, 1977. (1977) Zbl0352.34001MR0508721
  7. HALE J. K., KATO J., Phase space tor retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978),11-41. (1978) MR0492721
  8. HENRY D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. No 840, Springer-Verlag, 1981. (1981) Zbl0456.35001MR0610244
  9. HILLE E., PHILLIPS R. S., Functional Analysis and Semigroups, Amer. Math. Soc. Providence, 1957. (1957) Zbl0078.10004MR0089373
  10. KAPPEL F., SCHAPPACHER W., Some considerations to the fundamental theory of infinite delay equations, J. Diff. Eqs. 37 (1980), 141-183. (1980) Zbl0466.34036MR0587220
  11. KATO T., Perturbation Theory for Linear Operators, Springer-Verlag, 1966. (1966) Zbl0148.12601MR0203473
  12. KUNISH K., SCHAPPACHER W., Necessary conditions for partial differential equations with delay to generate C 0 - semigroup, J. Diff. Eqs. 50 (1983), 49-79. (1983) MR0717868
  13. NAITO T., On linear autonomous retarded equations with an abstract phase space for infinite delay, J. Diff. Eqs. 33 (1979), 74-91. (1979) Zbl0384.34042MR0540818
  14. NUSSBAUM R., The radius of the essential spectrum, Duke Math. J. 37 (1970), 473-478. (1970) Zbl0216.41602MR0264434
  15. SCHUMACHER K., On the resolvent of linear nonautonomous partial functional differential equations, preprint No 247, Universität Heidelberg, 1984. (1984) MR0807853
  16. SMULYAN Yu. L., Compact perturbation of operators, (in Russian), Doklady Akad. Nauk SSSR 101 (1955), 35-38. (1955) 

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