On the existence of periodic solutions of equations with a strongly increasing principal part. (English. Russian original) Zbl 1070.34023

Filippov, V. V.

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.

Reviewer: Ştefan Mirică (Bucureşti)

MSC:

34A60	Ordinary differential inclusions
34C25	Periodic solutions to ordinary differential equations

Keywords:

second-order differential inclusion; periodic solution; growth property