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On the existence of periodic solutions of equations with a strongly increasing principal part. (English. Russian original) Zbl 1070.34023
Sb. Math. 193, No. 11, 1707-1729 (2002); translation from Mat. Sb. 193, No. 11, 139-160 (2002).
Continuing previous work, the author proves first a large number of general topological and geometrical properties of solutions of second-order differential inclusions. Next, these properties are used to prove in Theorems 3.1 and 4.1 the existence of periodic solutions of scalar differential inclusions of the form $$x''\in F(t,x,x')$$ in the case $$F(t,x,x')\subseteq [-\gamma(x)-h(t),-\gamma(x)+h(t)]$$ where $$h(.)$$ is integrable and periodic and $$\gamma(.)$$ is continuous and satisfies certain growth conditions.

##### MSC:
 34A60 Ordinary differential inclusions 34C25 Periodic solutions to ordinary differential equations
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