• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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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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• v.34 no.3_4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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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.

• 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.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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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.