• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.437-442
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• 2014

In this paper we prove Ekeland's variational principle in the setting of locally complete spaces for lower semi continuous functions from above and bounded below. We use this theorem to prove Caristi's fixed point theorem in the same setting and also for lower semi continuous functions.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.359-380
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• 2017

This paper is concerned with a kind of boundary value problem for singular second order differential systems with Laplacian operators. Using a multiple fixed point theorem, sufficient conditions to guarantee the existence of at least three positive solutions of this kind of boundary value problem are established. An example is presented to illustrate the main results.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.775-782
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• 2002

In this paper we prove the existence of mild soultions for semilinear differential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.691-700
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• 2009

We prove the local existence of classical solutions of quasi-linear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.327-342
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• 2015

By employing a fixed point theorem in a weighted Banach space, we establish the existence of a solution for a system of impulsive singular fractional differential equations. Some examples are presented to illustrate the efficiency of the results obtained.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.57-69
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• 2012

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.1051-1065
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• 2012

In this paper, the global stability and almost periodicity are investigated for generalized Hopfield neural networks with time-varying neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results. Finally, an example is given to demonstrate the effectiveness of our results.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1145-1156
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• 2009

In this paper, we consider the existence, uniqueness of the solutions and controllability for the neutral functional integro-differential equations with delay terms by Sadovskii's fixed point theorem.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.737-746
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• 2017

In this paper, we discuss the existence theorem for multiple vortex solutions in the non-Abelian Chern-Simons-Higgs field theory developed by Aharony, Bergman, Jafferis, and Maldacena, on a doubly periodic domain. The governing equations are of the BPS type and derived by Auzzi and Kumar in the mass-deformed framework labeled by a continuous parameter. Our method is based on fixed point method.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.16-19
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• 2009

In this paper, we study the existence and uniqueness of solutions for the fuzzy differential equations in n-dimension fuzzy vector space $(E_N)^n$ using by Banach fixed point theorem.