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STABILITY OF SOLUTIONS TO NONLINEAR EVOLUTION PROBLEMS.
- Source :
-
Bulletin of Mathematical Analysis & Applications . 2022, Vol. 14 Issue 1, p28-30. 3p. - Publication Year :
- 2022
-
Abstract
- Let u0 = F(u; t); u(0) = u0; (1), u 2 H, H is a Hilbert space, F(u; t) is a nonlinear operator in H. If F(u; t) = A(t)u + B(u; t), where A(t) is a linear operator, B(u; t) = O(kuk2) for kuk ! 0, then problem (1) has a solution u = 0 if u0 = 0. If ku0k is small then the stability problem is: will the solution to (1) exist for all t > 0 and be small for all t > 0, A.M. Lyapunov gave in 1892 sufficient conditions for this to happen. In our paper a new technical tool is given for answering the above question. This tool (a nonlinear inequality) allows one to give old and new results on Lyapunov stability. One of such results is proved in this paper. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONLINEAR equations
*NONLINEAR operators
*LYAPUNOV stability
*LINEAR operators
Subjects
Details
- Language :
- English
- ISSN :
- 18211291
- Volume :
- 14
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Bulletin of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 156406256
- Full Text :
- https://doi.org/10.54671/BMAA-2022-1-3