Riassunto
Si costruiscono soluzioni limitate non triviali di una equazioneu'(t)=Au(t) (—∞<t<∞) doveA è il generatore di un semigruppo di operatori {T t;t≥0} tale cheT t converge fortemente verso 0 pert→∞.
Summary
We construct nontrivial bounded solutions of an abstract evolution equationu'(t)=Au(t) (—∞<t<∞) whereA generates a (C 0) semigroup of operators {T t;t≥0} such thatT t converges strongly to zero ast→∞.
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References
Hille E. andPhillips R. S.,Functional Analysis and Semi-groups, Amer. Math. Soc. Coll. Publ., Vol.31, Providence, R.I., 1957.
Zaidman S.,Bounded solutions of some abstract differential equations, Proc. Amer. Math. Soc.,23 (1969), 340–342.
Additional information
Supported by National Science Foundation grant GP-12722.
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Goldstein, J.A. On bounded solutions of abstract differential equations. Ann. Univ. Ferrara 16, 39–43 (1971). https://doi.org/10.1007/BF02825196
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DOI: https://doi.org/10.1007/BF02825196