scholarly journals Multivalued evolution equations with nonlocal initial conditions in Banach spaces

2007 ◽  
Vol 14 (3-4) ◽  
pp. 361-376 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Vasile Staicu
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Nonlocal Initial Conditions

scholarly journals Functional differential equations with nonlocal initial conditions

1997 ◽  
Vol 10 (2) ◽  
pp. 145-156 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Yun Gao
Keyword(s):  
Banach Spaces ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Cauchy Problems ◽  
Accretive Operators ◽  
Nonlocal Initial Conditions ◽  
Functional Differential

We study the existence, uniqueness, asymptotic properties, and continuous dependence upon data of solutions to a class of abstract nonlocal Cauchy problems. The approach we use is based on the theory of m-accretive operators and related evolution equations in Banach spaces.

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.

SEMILINEAR NONLOCAL PROBLEMS WITHOUT THE ASSUMPTIONS OF COMPACTNESS IN BANACH SPACES

2010 ◽  
Vol 08 (02) ◽  
pp. 211-225 ◽  
Author(s):  
XINGMEI XUE
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Differential System ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Problems ◽  
Hausdorff Measure Of Noncompactness ◽  
Nonlocal Initial Conditions

In this paper, we study the semilinear differential equations with nonlocal initial conditions in the separable Banach spaces. We derive conditions expressed in terms of the Hausdorff measure of noncompactness under which the mild solutions exit. For illustration, a partial integral differential system is worked out.

Nonlocal problem for fractional stochastic evolution equations with solution operators

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Pengyu Chen ◽  
Xuping Zhang ◽  
Yongxiang Li
Keyword(s):  
Hilbert Spaces ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Problem ◽  
Growth Conditions ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Nonlocal Initial Conditions ◽  
Analysis Theory

AbstractIn this article, we are concerned with a class of fractional stochastic evolution equations with nonlocal initial conditions in Hilbert spaces. The existence of mild solutions is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions by using fractional calculations, Schauder fixed point theorem, stochastic analysis theory,

scholarly journals Existence of Solutions in Some Interpolation Spaces for a Class of Semilinear Evolution Equations with Nonlocal Initial Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Jung-Chan Chang ◽  
Hsiang Liu
Keyword(s):  
Evolution Equations ◽  
Existence Of Solutions ◽  
Initial Conditions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Strong Solutions ◽  
Interpolation Spaces ◽  
Nonlocal Initial Conditions ◽  
Densely Defined ◽  
Semilinear Evolution Equations

This paper is concerned with the existence of mild and strong solutions for a class of semilinear evolution equations with nonlocal initial conditions. The linear part is assumed to be a (not necessarily densely defined) sectorial operator in a Banach spaceX. Considering the equations in the norm of some interpolation spaces betweenXand the domain of the linear part, we generalize the recent conclusions on this topic. The obtained results will be applied to a class of semilinear functional partial differential equations with nonlocal conditions.

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