Abstract
II G(u)ll <=g, u e g (3) jor some constant K, (4) G has a strong sub-asymptote l :Ker A-~ IR. By strong sub-asymptote we mean the following: Let Vbe a linear subspace of a Banach space B and G:B~B* be a mapping from B into its dual (respectively, from a Hilbert space into itself). G is said to have the strong sub-asymptote 1: V~IR iJ l(v):<liminf(G(u~), llujIIluj) U--* oe) (5) Jor every sequence (u~) such that JJ u~lt-'* go and II u j I]l u j~v weakly ( j ~ oe), v +-O, v~V. With these hypotheses one can formulate the following Landesman-Lazer type theorem
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