• Korean Journal of Mathematics
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• v.20 no.4
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• pp.507-515
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• 2012

We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three dimensional subspace with three axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.503-511
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• 2010

We prove a common fixed point theorem for S-contraction mappings without continuity. Using this result we obtain an approximating curve for S-nonexpansive mappings in a Banach space and prove Browder's type strong convergence theorem for this approximating curve. The demiclosedness principle for S-nonexpansive mappings is also established.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.633-644
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• 2014

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.509-517
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• 2005

We shall prove the existence and uniqueness theorem of a solution to the non local fuzzy differential equation using the contraction mapping principle.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.321-325
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• 2007

We prove the Medina's results about the existence and uniqueness of solutions of discrete Volterra equations of convolution type in weighted spaces, by using the well-known Contraction Mapping Principle.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.58-63
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• 1998

We will prove the existence and uniqueness theorem of solutions to the nonlocal fuzzy integro-differential equations using Contraction mapping principle.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.517-526
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• 2024

In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.255-268
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• 2005

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.101-110
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• 2006

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green's functions and contraction mapping principle.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.79-91
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• 2010

In this paper, a class of fractional integrodifferential equations of mixed type with nonlocal conditions is considered. First, using contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. Second, the existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with nonlocal conditions is also presented.