Trichotomy and bounded solutions of nonlinear differential equations. (English) Zbl 0819.34040

Cichoń, Mieczysław

Math. Bohem. 119, No. 3, 275-284 (1994).

This article presents new existence results of bounded solutions for the quasilinear differential equation \(x' = A(t)x + f(t,x)\) \((- \infty < t < \infty)\) provided that the linear part \(x' = A(t)x\) \((- \infty < t < \infty)\) is trichotomic and the nonlinearity \(f(t,x)\) satisfies a variant Darboux condition with respect to a noncompactness measure \(\chi\).

Reviewer: P.Zabreiko (Minsk)

MSC:

34G20	Nonlinear differential equations in abstract spaces
34C11	Growth and boundedness of solutions to ordinary differential equations

Keywords:

existence; bounded solutions; quasilinear differential