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Evolution Generated by continuous Dissipative Plus Compact Operators
Author(s) -
Schechter Eric
Publication year - 1981
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/13.4.303
Subject(s) - mathematics , banach space , dissipative system , pure mathematics , evolution equation , range (aeronautics) , space (punctuation) , nonlinear system , dissipative operator , discrete mathematics , mathematical analysis , physics , materials science , quantum mechanics , composite material , linguistics , philosophy
Let B and C be continuous nonlinear operators in a Banach space. Assume that B satisfies a dissipativeness condition, and that the range of C is relatively compact. Some sufficient conditions are given for the existence of solutions of the equation u ′( t ) = B ( t , u ( t )) + C ( t , u ( t )).