• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.561-568
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• 2007

In this paper, we improve the results of [9] and give an application to boundedness of the solutions of nonlinear integro-differential equations.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.137-149
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• 2001

In this paper we consider some nonlinear parabolic partial differential equations with distributed deviating arguments and establish sufficient conditions for the oscillation of some boundary value problems.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.559-571
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• 2004

The aim of the present paper is to establish some nonlinear integral inequalities in two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential equations.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.393-400
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• 2011

In this paper we study h-stability for the linear impulsive equations using the notion of kinematical similarity and impulsive integral inequality.

• East Asian mathematical journal
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• v.10 no.1
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• pp.79-83
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• 1994

• East Asian mathematical journal
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• v.9 no.1
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• pp.99-104
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• 1993

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1471-1484
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• 2020

It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bi-drifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.447-454
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• 2014

Two necessary and sufficient conditions for the oscillation of the bounded solutions of the second-order nonlinear delay differential equation $$(a(t)x^{\prime}(t))^{\prime}+q(t)f(x[{\tau}(t)])=0$$ are obtained by constructing the sequence of functions and using inequality technique.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.11
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• pp.2023-2026
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• 2007

In this letter, the problem for a class of neutral differential equation is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both ${\tau}\;and\;{\sigma}$, is derived in terms of linear matrix inequality (LMI). Two numerical examples are carried out to support the effectiveness of the proposed method.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.197-208
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• 2024

In the present paper, we establish Ulam-Hyres and Ulam-Hyers-Rassias stabilities for nonlinear impulsive integro-differential equations with non-local condition in Banach space. The generalization of Grownwall type inequality is used to obtain our results.