• 대한수학회보
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• 제53권4호
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• pp.1095-1103
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• 2016

B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

• 충청수학회지
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• 제26권4호
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• pp.811-819
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• 2013

In this paper we investigate h-stability for linear impulsive equations using the notion of $t_{\infty}$-similarity and an impulsive integral inequality.

• 충청수학회지
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• 제25권3호
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• pp.589-597
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• 2012

In this paper we investigate the stability of solutions of the perturbed differential equations with the positive order of the perturbation by using the notion of the Lyapunov exponent of unperturbed equations and an integral inequality of Bihari type.

• East Asian mathematical journal
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• 제30권1호
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• pp.79-91
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• 2014

We consider the parabolic evolution differential equation such as heat equation and porus-medium equation on a Riemannian manifold M whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by 0 on some amount of M. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.377-385
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• 2007

In this paper, by the equations of Mao [9] and Peng [5], we use the martingale method to establish the comparison theorems of backward stochastic differential equations (BSDEs). We generalize the results of Cao-Yan [1].

• 충청수학회지
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• 제34권3호
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• pp.221-234
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• 2021

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.305-316
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• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

• 대한수학회지
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• 제49권6호
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• pp.1163-1174
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• 2012

This paper examines a temperature dependent Stokes flow in a semi-infinite cylinder. Under appropriate initial and boundary conditions the author establishes exponential decay of solutions in energy norm with distance from the finite end of the cylinder.

• Korean Journal of Mathematics
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• 제11권2호
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• pp.117-125
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• 2003

Let $x(t)$ satisty $$(p(t)x^{\prime}(t))^{\prime}+q(t)x^{{\alpha}}(t)+r(t)x^{{\beta}-1}x^{\prime}(t){\leq}0({\geq}0)$$. Then the zeros of $x(t)$ or $x^{\prime}(t)$ are simple.

• 대한수학회보
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• 제52권5호
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• pp.1753-1757
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• 2015

In this note we obtain a unique continuation result for the differential inequality ${\mid}\bar{\partial}u{\mid}{\leq}{\mid}Vu{\mid}$, where $\bar{\partial}=(i{\partial}_y+{\partial}_x)/2$ denotes the Cauchy-Riemann operator and V (x, y) is a function in $L^2(\mathbb{R}^2)$.