Linearized stability for nonlinear evolution equations

Journal of Evolution Equations

Volumn 3, Issue 2, 2003, Pages 361-373

  Ruess, Wolfgang M ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Accretive operators; Linearized stability; Nonlinear evolution equations; Partial differential delay equations

Indexed keywords

PSITTIROSTRA PSITTACEA;

EID: 0141760346     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/978-3-0348-7924-8_19     Document Type: Article

References (11)

1. BÉNILAN, P., CRANDALL, M. G. and PAZY, A., Evolution Equations Governed by Accretive Operators. Monograph, in preparation.
2. DESCH, W. and SCHAPPACHER, W., Linearized stability for nonlinear semigroups. In: Differential Equations in Banach Spaces (A. Favini and E. Obrecht, Eds.), 61-73, Lecture Notes in Math. vol. 1223, Springer, New York, 1986.
3. KATO, N., A principle of linearized stability for nonlinear evolution equations, Trans. Amer. Math. Soc. 347 (1995), 2851-2868.
4. MIYADERA, I., Nonlinear Semigroups, Transl. of Math. Monographs 109, Amer. Math. Soc. Providence, RI, 1992.
5. PIERRE, M., Perturbations localement Lipschitziennes et continues d'opérateurs m-accrétifs, Proc. Amer. Math. Soc. 58 (1976), 124-128.
6. RAUCH, J., Stability of motion for semilinear equations. In: Boundary Value Problems for Linear Evolution Partial Differential Equations (H.G. Garnir, Ed.), 319-349, D. Reidel Publ. Comp. Dordrecht, 1977.
7. RUESS, W. M., Existence and stability of solutions to partial functional differential equations with delay, Adv. Diff. Eqns. 4 (1999), 843-876.
8. RUESS, W. M. and SUMMERS, W. H., Linearized stability for abstract differential equations with delay, J. Math. Anal. Appl. 198 (1996), 310-336.
9. SMOLLER, J., Shock Waves and Reaction-Diffusion Equations, Grundlehren Math. Wiss. 258, Springer, New York, 1983.
10. WEBB, G.F., Theory of nonlinear age-dependent population dynamics, Marcel-Dekker, New York, 1985.
11. ZEIDLER, E., Nonlinear Functional Analysis and Applications, vol. I, Springer, New York, 1986.