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Existence problems in second order evolution inclusions: discretization and variational approach. (English) Zbl 1173.35302

The authors consider a second order evolution inclusion with delay. The proofs of two existence results presented in the paper are based on a discretization techniques and involve the multivalued Scorza Dragoni theorem and multivalued Dugundji extension theorem. Finally some applications are indicated involving variational techniques, biting lemma, the characterization of the second dual of \(L^1_{\mathbb R^d}\) and Young measures.

MSC:

35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
47H04 Set-valued operators
35R10 Partial functional-differential equations
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