Article
Keywords:
linearization; stability; variational inequality
Summary:
It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
References:
[1] J. P. Aubin A. Cellina:
Differential Inclusions. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1984.
MR 0755330
[3] P. Drábek M. Kučera:
Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions. Czech. Math. J. 36 (111) (1986), 116-130.
MR 0822872
[4] P. Drábek M. Kučera:
Reaction-diffusion systems: Destabilizing effect of unilateral conditions. Nonlinear Analysis, Theory, Methods & Applications 12 (1988), no. 11, 1173-1192.
DOI 10.1016/0362-546X(88)90051-X |
MR 0969497
[5] H. Gajewski K. Gröger K. Zacharias:
Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin, 1974.
MR 0636412
[6] J. Neustupa:
The linearized uniform asymptotic stability of evolution differential equations. Czech. Math. J. 34 (109) (1984), 257-284.
MR 0743491 |
Zbl 0599.34081
[7] M. Kučera J. Neustupa:
Destabilizing effect of unilateral conditions in reaction-diffusion systems. Commentationes Math. Univ. Carolinae 27 (1986), no. 1, 171-187.
MR 0843429