• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.253-265
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• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1123-1139
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• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.949-968
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• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.2
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• pp.93-105
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• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1093-1103
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• 2011

We give the characterizations of the classes of matrix trans-formations ($m(\phi),{\ell}_p$), ($n(\phi),{\ell}_p$) ([5, Theorem 2]), (${\ell}_p,m(\phi)$) ([5, Theorem 1]) and (${\ell}_p,n(\phi)$) for $1{\leq}p{\leq}{\infty}$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.229-242
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• 2020

Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.