Continuous Selections of Solution Sets to Second Order Evolution Equations
نویسنده
چکیده
We prove the existence of a continuous selection of the multivalued map ) η , ξ ( → AF ) η , ξ ( , where AF ) η , ξ ( is the set of all mild solutions of the Cauchy problem x” ∈ Ax + F(t, x) , x (0) = ξ , x (0) = η assuming that F is Lipschitzian with respect to x and A is the infinitesimal generator of a strongly cosine family of linear operators on a Banach space E. AMS 2000 Subject Classification: Primary 35G25, 47D09. Secondary 47D04, 24C60
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