# Schaefer type theorem and periodic solutions of evolution equations

@article{Liu2006SchaeferTT, title={Schaefer type theorem and periodic solutions of evolution equations}, author={Yicheng Liu and Zhixian Li}, journal={Journal of Mathematical Analysis and Applications}, year={2006}, volume={316}, pages={237-255} }

## 44 Citations

CRITICAL KRASNOSELSKII-SCHAEFER TYPE FIXED POINT THEOREMS FOR WEAKLY SEQUENTIALLY CONTINUOUS MAPPINGS AND APPLICATION TO A NONLINEAR INTEGRAL EQUATION

- Mathematics
- 2016

In this paper, we first state some new fixed point theorems for operators of the form A + B on a bounded closed convex set of a Banach space, where A is a weakly compact and weakly sequentially…

Integrable solutions of a nonlinear functional integral equation on an unbounded interval

- Mathematics
- 2009

Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

- Mathematics
- 2012

A FIXED POINT THEOREM OF KRASNOSELSKII-SCHAEFER TYPE AND ITS APPLICATIONS IN CONTROL AND PERIODICITY OF INTEGRAL EQUATIONS

- Mathematics
- 2011

In this paper, we prove a fixed point theorem for the sum of a nonlinear contraction mapping and compact operator. The fixed point theorem obtained here resembles that of Krasnosel- skii in which the…

Existence and asymptotic stability of periodic solution for evolution equations with delays

- Mathematics
- 2011

Second Order Impulsive Neutral Functional Differential Inclusions

- Mathematics
- 2008

Abstract. In this paper, we investigate the existence of solutions of second order im-pulsive neutral functional diﬀerential inclusions which the nonlinearity F admits convexand non-convex values.…

Periodic Solutions of Singular Integral Equations

- Mathematics
- 2011

We consider a scalar integral equation x(t) = a(t) ― ∫ t ―∞ C(t, s) g(s,x(s))ds in which C(t, s) has a singularity at t = s. There are periodic assumptions on a, C, and g. First we prove a fixed…

Periodicity in Neutral Functional Differential Equations by Direct Fixed Point Mapping

- Mathematics
- 2008

Burton-Kirk's fixed point theorem or degree theory is used to study the existence of periodic solutions in neutral functional differential equations by con- structing a homotopy which is a…

Krasnoselskii type fixed point theorems and applications

- Mathematics
- 2007

In this paper, we establish two fixed point theorems of Krasnoselskii type for the sum of A + B, where A is a compact operator and I - B may not be injective. Our results extend previous ones. As an…

Applicable Analysis and Discrete Mathematics

- Mathematics
- 2013

In this paper, we establish some new existence, uniqueness and Ulam-Hyers stability theorems for coincidence problems for two single-valued mappings. The main results of this paper extend the results…

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