Solutions For Impulsive Evolution Equations Research Articles

Existence of periodic solutions for impulsive evolution equations in ordered Banach spaces

In this paper, we use the perturbation method and the mixed monotone iterative technique to discuss the existence of periodic solutions for impulsive evolution equations in ordered Banach spaces. Under impulsive functions satisfying broader monotone conditions and without assumption that the lower and upper solutions exist, we obtain the existence results of ω-periodic mild solutions. Moreover, an application is given to illustrate our theoretical results.

Variational approach to impulsive evolution equations

This article uses variational method for studying existence and uniqueness of solutions for impulsive evolution equations. The main techniques include Hilbert triple, Sobolev embedding theorem, Galerkin approximation and weak convergence for passing to the limit.

Mixed Monotone Iterative Technique for Abstract Impulsive Evolution Equations in Banach Spaces

By constructing a mixed monotone iterative technique under a new concept of upper and lower solutions, some existence theorems of mild -periodic ( -quasi) solutions for abstract impulsive evolution equations are obtained in ordered Banach spaces. These results partially generalize and extend the relevant results in ordinary differential equations and partial differential equations.

Measure solutions for impulsive evolution equations with measurable vector fields

In this paper we present some results on the question of existence of generalized or measure valued solutions for semilinear impulsive evolution equations on Banach spaces with the nonlinear parts being merely measurable and bounded on bounded sets. This is a far reaching generalization of the previous results of the author and others. It may be interesting to consider extension of the results of this paper to cover impulsive differential inclusions and their potential applications to control theory and uncertain dynamics.