• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.593-606
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• 2002

We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.513-522
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• 2013

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.739-751
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• 2010

This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.137-143
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• 2001

In this paper, we study the existence, uniqueness and norm estimate of solutions for the nonlinear delay integro-differential system.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.349-356
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• 2005

In this paper, by using the Leray-Schauder continuation theorem and Wirtinger-type inequalities, we establish the existence and uniqueness theorems for two-point boundary value problems of a certain class of fourth-order nonlinear differential equations.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.175-187
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• 2002

The existence and uniqueness of steady states for the age structured S-I-R epidemic model is considered. Intercohort form with external force is considered for the force of infection. Existence is obtained for nonvanishing external force of infection. Uniqueness is shown for the case where there is no vertical transmission of the disease.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.647-671
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• 2020

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.191-202
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• 2019

The aim of this paper is to develop a monotone iterative technique by introducing upper and lower solutions to Riemann-Liouville fractional differential equations with deviating arguments and integral boundary conditions. As an application of this technique, existence and uniqueness results are obtained.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.895-902
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• 2009

In this paper, the singular three-point boundary value problem $$\{{{u"(t)\;+\;f(t,\;u)\;=\;0,\;t\;{\in}\;(0,\;1),}\atop{u(0)\;=\;0,\;u(1)\;=\;{\alpha}u(\eta),}}\$$ is studied, where 0 < $\eta$ < 1, $\alpha$ > 0, f(t,u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.877-894
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• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.