• 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.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.305-309
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• 1997

In this paper we prove the existence of a special type of multivortex solutions of $SU (N)_g \times U(1)_l$ Chern-Simons model. More specifically we prove existence of solutions of the self-duality equations for $(\Phi(x), j =1, \cdots, N$ has the same zeroes. In this case we find that the equation can be reduced to the single semilinear elliptic partial differential equations studied by Caffarelli and Yang.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.565-572
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• 2019

In this paper, we consider a Korteweg-de Vries equation in noncylindrical domain. This work is devoted to prove existence and uniqueness of global solutions employing Faedo-Galerkin's approximation and transformation of the noncylindrical domain with moving boundary into cylindrical one. Moreover, we estimate the exponential decay of solutions in the asymptotically cylindrical domain.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.339-358
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• 2000

Let be a bonded domain in N with smooth boundary . In this paper, we consider the existence of solutions of the following problem: (1.1)-div{} - + = , , , , , , where q > 1, p$\geq$1, $\delta$>0, , the Laplacian in N and is a positive function like as .

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.169-178
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• 2005

In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in $\mathbb{R}^2$. After reducing to semilinear elliptic partial differential equations, we show the existence of topological solutions using iteration and variational arguments & prove that there is a sequence of topological solutions which converges locally uniformly to a constant as the Chern­Simons coupling constant goes to zero and the convergence is exponentially fast.

• 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.

• East Asian mathematical journal
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• v.38 no.5
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• pp.593-601
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• 2022

In this paper, we consider singular 𝜑-Laplacian problems with nonlocal boundary conditions. Using a fixed point index theorem on a suitable cone, the existence results for one or two positive solutions are established under the assumption that the nonlinearity may not satisfy the L¹-Carathéodory condition.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.609-624
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• 1996

Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

• East Asian mathematical journal
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• v.30 no.5
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• pp.631-637
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• 2014

In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.35-64
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• 2021

In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.