On impulsive hyperbolic differential inclusions with nonlocal initial conditions. (English) Zbl 1159.49042

Summary: This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases.


49N25 Impulsive optimal control problems
49J20 Existence theories for optimal control problems involving partial differential equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
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