Application of Rothe's method to nonlinear evolution equations
In the present paper initial operators for a right invertible operator, which are induced by sequential shifts and have the property c(R) are constructed. An application to the Lagrange type interpolation problem is given. Moreover, an example with the Pommiez operator is studied.
We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions.
We apply Aupetit's scarcity theorem to obtain stronger versions of many spectral-theoretical results in ordered Banach algebras in which the algebra cone has generating properties.
In the paper [13] we proved a fixed point theorem for an operator , which satisfies a generalized Lipschitz condition with respect to a linear bounded operator , that is: The purpose of this paper is to show that the results obtained in [13], [14] can be extended to a nonlinear operator .