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Equivariant degree of convex-valued maps applied to set-valued BVP

100%

Dzedzej Z.

Open Mathematics

2012

tom 10

nr 6

2173-2186

An equivariant degree is defined for equivariant completely continuous multivalued vector fields with compact convex values. Then it is applied to obtain a result on existence of solutions to a second order BVP for differential inclusions carrying some symmetries.

Filippov Lemma for certain second order differential inclusions

100%

Bartuzel G., Fryszkowski A.

Open Mathematics

2012

tom 10

nr 6

1944-1952

In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y′(0) = 0, where the matrix A ∈ ℝd×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y 0 ∈ W 2,1 be an arbitrary function fulfilling the above initial conditions and such that where p 0 ∈ L 1[0, 1]. Then there exists a solution y ∈ W 2,1 to the above differential inclusions such that a.e. in [0, 1], .

Ograniczanie wyników

2 Open Mathematics

1 Bartuzel G.

1 Dzedzej Z.

1 Fryszkowski A.

2 2012

Wyniki wyszukiwania

Equivariant degree of convex-valued maps applied to set-valued BVP

Filippov Lemma for certain second order differential inclusions