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Filippov Lemma for matrix fourth order differential inclusions

Grzegorz Bartuzel, Andrzej Fryszkowski (2014)

Banach Center Publications

In the paper we give an analogue of the Filippov Lemma for the fourth order differential inclusions y = y”” - (A² + B²)y” + A²B²y ∈ F(t,y), (*) with the initial conditions y(0) = y’(0) = y”(0) = y”’(0) = 0, (**) where the matrices A , B d × d are commutative and the multifunction F : [ 0 , 1 ] × d c l ( d ) is Lipschitz continuous in y with a t-independent constant l < ||A||²||B||². Main theorem. Assume that F : [ 0 , 1 ] × d c l ( d ) i s m e a s u r a b l e i n t a n d i n t e g r a b l y b o u n d e d . L e t y₀ ∈ W4,1 b e a n a r b i t r a r y f u n c t i o n s a t i s f y i n g ( * * ) a n d s u c h t h a t ...

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