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

 Access to full text

 Full (PDF)

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) 

1. Ľubica Šedová, Parabolic equations with deviating argument in advance
2. Lubica Kossaczká, Integral manifold of the parabolic differential equation with deviating argument
3. Hana Petzeltová, Solution semigroup and invariant manifolds for functional equations with infinite delay