Weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions

2009 ◽  
Vol 215 (5) ◽  
pp. 1647-1652 ◽  
Author(s):  
Jing-huai Liu ◽  
Xiao-qiu Song ◽  
Ping-li Zhang
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic ◽  
Semilinear Evolution Equations

scholarly journals Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Abdelkarim-Nidal Akdad ◽  
Khalil Ezzinbi ◽  
Lotti Souden
Keyword(s):  
Existence Result ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic ◽  
Automorphic Functions

AbstractIn this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.

scholarly journals Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Zhang ◽  
Ti-Jun Xiao ◽  
Jin Liang
Keyword(s):  
Existence Theorem ◽  
Evolution Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Exponentially Stable ◽  
Pseudo Almost Periodic ◽  
Semilinear Evolution Equations ◽  
Composition Theorem

We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation:x′(t)=Ax(t)+f(t,x(t)),t∈ℝ, whereAis the infinitesimal generator of an exponentially stableC0-semigroup. An application is also given to illustrate the abstract existence theorem.

Pseudo Almost Periodicity and Its Applications to Impulsive Nonautonomous Partial Functional Stochastic Evolution Equations

2018 ◽  
Vol 19 (5) ◽  
pp. 511-529
Author(s):  
Zuomao Yan ◽  
Xiumei Jia
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Almost Periodic ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Pseudo Almost Periodic Functions ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic ◽  
Lipschitz Conditions ◽  
Composition Theorem

AbstractIn this paper, we establish a new composition theorem for pseudo almost periodic functions under non-Lipschitz conditions. We apply this new composition theorem together with a fixed-point theorem for condensing maps to investigate the existence of$p$-mean piecewise pseudo almost periodic mild solutions for a class of impulsive nonautonomous partial functional stochastic evolution equations in Hilbert spaces, and then, the exponential stability of$p$-mean piecewise pseudo almost periodic mild solutions is studied. Finally, an example is given to illustrate our results.

Fractional evolution equations with nonlocal conditions in partially ordered Banach space

2018 ◽  
Vol 34 (3) ◽  
pp. 379-390
Author(s):  
HEMANT KUMAR NASHINE ◽  
◽  
HE YANG ◽  
RAVI P. AGARWAL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Coupled Fixed Point ◽  
Positive Cone ◽  
Bounded Linear ◽  
Partially Ordered ◽  
C0 Semigroup ◽  
Uniformly Bounded

In the present work, we discuss the existence of mild solutions for the initial value problem of fractional evolution equation of the form where C Dσ t denotes the Caputo fractional derivative of order σ ∈ (0, 1), −A : D(A) ⊂ X → X generates a positive C0-semigroup T(t)(t ≥ 0) of uniformly bounded linear operator in X, b > 0 is a constant, f is a given functions. For this, we use the concept of measure of noncompactness in partially ordered Banach spaces whose positive cone K is normal, and establish some basic fixed point results under the said concepts. In addition, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. We also supply some new coupled fixed point results via MNC. To justify the result, we prove an illustrative example that rational of the abstract results for fractional parabolic equations.

scholarly journals Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 792-805
Author(s):  
Junfei Cao ◽  
Zaitang Huang
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Initial Conditions ◽  
Asymptotically Periodic ◽  
Semilinear Evolution Equations ◽  
Asymptotically Periodic Solutions

AbstractIn this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.

Sign in / Sign up

Export Citation Format

Share Document