This article is cited in 22 papers

The method of local linear approximation in the theory of nonlinear functional-differential equations

V. E. Slyusarchuk

Ukranian State Academy of Water Economy

Abstract: Conditions for the existence of solutions to the nonlinear functional-differential equation
$$ \frac{d^mx(t)}{dt^m}+(Fx)(t)=h(t), \qquad t\in\mathbb R, $$
in the space of functions bounded on the axes are obtained by using local linear approximation to the operator $F$.
Bibliography: 21 items.

Keywords: functional-differential equations, invertibility of nonlinear operators.

UDC: 517.929

MSC: 34C11, 47J05

Received: 20.03.2009

DOI: 10.4213/sm7562

 English version: Sbornik: Mathematics, 2010, 201:8, 1193–1215

Bibliographic databases:

• 
• 
• 
• 
• 
•