A. R. Abdullaev, E. V. Plekhova
abstract:
The parameter continuation method plays an important role in the theory of
linear operators and linear boundary value problems. This method is based on
Schauder's theorem on the invertibility of the sum of two linear operators, the
first of which is invertible and the sum satisfies a certain condition. In the
present paper, the mentioned assertion is extended for arbitrary steady
properties of linear operators. The corresponding information related to steady
properties and examples of steady properties are given. An example of applying
the obtained assertions is presented.
Mathematics Subject Classification: 45A05, 45D05, 47A55
Key words and phrases: Schauder's theorem, parameter continuation method, steady property