• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.45-60
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• 2015

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the results.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.49-58
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• 2016

We study the existence of S-asymptotically ${\omega}$-periodic mild solutions of partial functional integrodifferential equation by the method of Caicedo et al. [2].

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.351-363
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• 2020

We introduce a new concept of Stepanov weighted pseudo almost periodic functions of class r which have been established by recently in [20]. Furthermore, we study the uniqueness and existence of Stepanov weighted pseudo almost periodic mild solutions of partial neutral functional differential equations having the Stepanov pseudo almost periodic forcing terms on finite delay.

• Journal of Korean Public Health Nursing
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• v.30 no.2
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• pp.259-273
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• 2016

Purpose: The purpose of this study was to explore the barriers and solution of providing long-term care (LTC) services at home for the beneficiaries with mild dementia. Methods: The data were collected by interviewing three focus groups consisting of 10 home-visit nurses and analyzed through the analytic process by Morgan and Krueger. Results: The barriers of providing LTC services for clients were identified as follows: inadequateness of the current LTC model for elderly individuals with mild dementia and inappropriateness of the personal environment for home care. The solutions for these barriers were suggested as follows: building up a safe environment for home care and maintaining an appropriate standard utilization plan of LTC service. Conclusion: The current service model for the beneficiaries with mild dementia should be modified in order to provide comprehensive long-term care services based on their complex needs.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.909-943
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• 2017

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.585-597
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• 2011

We prove the existence and uniqueness of classical solutions for a quasilinear delay integrodifferential equation in Banach spaces. The result is established by using the semigroup theory and the Banach fixed point theorem.

• 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.

• East Asian mathematical journal
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• v.19 no.1
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• pp.91-102
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• 2003

In this paper we prove the existence of mild and strong solutions of nonlinear delay integrodifferential equations with nonlocal conditions. The results are obtained by using the Schauder fixed point theorem and resolvent operator.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.71-77
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• 2022

This work considers the existence and uniqueness of fuzzy solutions for impulsive abstract partial neutral functional differential systems. To establish the existence and uniqueness, we apply the concept of impulse, semi group theory and suitable fixed point theorem.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.1
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• pp.81-87
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• 1994

The mild slope equation has been directly derived from the energy equation, and the relation between energy equation and Green's first and second identities was also clarified. It is shown here that the mild slope equation of elliptic type in the wave-current interaction has to have the same form as the one derived by Berkhoff (1972), and its physical meaning was investigated through analytical solutions.