This paper proposes an abstract theory concerned with dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to construct global attractors, an approach based on the notion of generalized semiflow is employed instead of the usual semi-group approach, since solutions o...

where 0 ≤ t0 < t1 < ··· < tp ≤ a, a > 0, −A is the infinitesimal generator of aC0-semigroup in a Banach space X , u0 ∈ X , and f : [0,a]×X → X , g : [0,a]p ×X → X are given functions. Subsequently he has investigated the same type of problem for different kinds of evolution equations in Banach spaces [10, 11, 12, 13, 14]. Ntouyas and Tsamatos [31] have established the global existence of soluti...

‎In this paper‎, ‎we prove some theorems related to properties of‎ ‎generalized symmetric hybrid mappings in Banach spaces‎. ‎Using Banach‎ ‎limits‎, ‎we prove a fixed point theorem for symmetric generalized‎ ‎hybrid mappings in Banach spaces‎. ‎Moreover‎, ‎we prove some weak‎ ‎convergence theorems for such mappings by using Ishikawa iteration‎ ‎method in a uniformly convex Banach space.

This paper is concerned with sufficient conditions for the controllability for nonlocal nonlinear impulsivefuzzy stochastic systems in Banach space by using the concept of Mild solution. And the conditions are drive by using Sadovskii fixed point theorem, Hausdorff measure of noncompactness and operator semigroup. 1. Introduction The problem of controllability is to show the existence ofa contr...

The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given. 1. Introduction. The fixed point technique is widely used as a tool to study the controllability of nonlinear systems in finite-and infinite-dimensi...

This paper is concerned with the existence of mild solutions to a class of semilinear differential inclusions with nonlocal conditions. By using the fixed point theory for multivalued maps, we get some general results on nonlocal differential inclusions, which include some recent results on nonlocal problems as special cases. An example of partial differential equations is provided to illustrat...

A class of semilinear evolution equations of the second order in time of the form utt+Au+μAut+Autt = f(u) is considered, where −A is the Dirichlet Laplacian, Ω is a smooth bounded domain in RN and f ∈ C1(R,R). A local well posedness result is proved in the Banach spacesW 1,p 0 (Ω)×W 1,p 0 (Ω) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies an addi...

* Correspondence: lpzmath@yahoo. com.cn School of Mathematics, Yangzhou University, Yangzhou 225002, China Abstract This article is concerned with impulsive semilinear differential equations with nonlocal initial conditions in Banach spaces. The approach used is fixed point theorem combined with the technique of operator transformation. Existence results are obtained when the nonlocal item is L...

In this paper, the existence of a mild solution to Cauchy problem for impulsive semilinear second-order differential inclusion in Banach space is investigated case when nonlinear term also depends on first derivative. This purpose achieved by combining Kakutani fixed point theorem with approximation solvability method and weak topology. combination enables obtaining result under easily verifiab...