• 충청수학회지
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• 제23권1호
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• pp.137-147
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• 2010

In this paper we extend a differential inequality presented in Theorem 2.2 [6] to a dynamic inequality on time scales.

• 충청수학회지
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• 제3권1호
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• pp.115-120
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• 1990

We obtain one simple generalization of the Gronwall's inequality by using the Viswanatham's theorem.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.193-206
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• 2016

In this paper, we study boundary value problems for fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

• 충청수학회지
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• 제31권1호
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• pp.161-166
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• 2018

This paper deals an impulsive fractional integral inequality with singular kernel which can be used in getting the explicit estimate of solutions of impulsive fractional differential equations.

• 대한수학회보
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• 제42권4호
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• pp.789-805
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• 2005

In this paper we consider analogous of Gronwall-type inequalities involving iterated integrals in the inequality (1.2) for functions when the function u in the right-hand side of the in­equality (1.2) is replaced by the function $u^P$ for some p. These inequalities are effective tools in the study of a system of an integral equation. We also provide some integral inequalities involving iterated integrals.

• 충청수학회지
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• 제20권4호
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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.

• 대한수학회논문집
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• 제16권2호
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• pp.225-233
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• 2001

In this paper, we establish the energy inequalities for second order quasilinear hyperbolic mixed problems in the domain R_(sup)n.

• 대한수학회보
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• 제50권1호
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• pp.275-283
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• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

• 충청수학회지
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• 제26권1호
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• pp.71-84
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• 2013

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

• 대한수학회지
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• 제43권3호
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• pp.563-578
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• 2006

The main aim of the present paper is to establish some new Gronwall type inequalities involving iterated integrals and give some applications of the main results.