Anti-periodic solutions for nonlinear evolution inclusions
Tóm tắt
We consider an anti-periodic evolution inclusion defined on an evolution triple of spaces, driven by an operator of monotone-type and with a multivalued reaction term F(t, x). We prove existence theorem for the “convex” problem (that is, F is convex-valued) and for the “nonconvex” problem (that is, F is nonconvex-valued) and we also show the existence of extremal trajectories (that is, when F is replaced by
$$\mathrm {ext}\,F$$
). Finally, we prove a “strong relaxation” theorem, showing that the extremal trajectories are dense in the set of solutions of the convex problems.
Tài liệu tham khảo
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