• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.73-82
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• 2018

In this article we consider certain types of nonlinear matrix equations including the stochastic rational Riccati equation and show the existence and uniqueness of the positive definite solution by using Bhaskar-Lakshmikantham's coupled fixed point theorem.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.511-526
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• 2008

In this paper, we consider an elliptic system of three equations using the minimax theorem. We prove the existence of two solutions for suitable forcing terms, under a condition on the linear part which prevents resonance with eigenvalues of the operator.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.433-440
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• 2002

In this paper, we first prove the existence of fixed points for fuzzy mappings that satisfy a certain contractive condition. Also, we give a fixed point theorem for generalized contractive fuzzy mapping by using Caristi's by fixed point theorem.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.131-144
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• 2020

Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni-Salce [7] and Bazzoni [4], are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs-Salce [14], showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem 3.7). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair (𝒫₁, 𝒟) (Theorem 4.1). Similar characterization is proved concerning the existence of divisible envelopes for h-local rings in the same class (Theorem 5.3). In addition, Bazzoni's characterization via direct sums of weak-injective modules [4] is extended to all commutative rings (Theorem 6.4). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.

• East Asian mathematical journal
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• v.25 no.4
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• pp.505-516
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• 2009

In this paper, we consider a new class of generalized mixed vector equilibrium-like problems in Banach spaces. By using Fan-KKM Theorem and Nadler's Theorem, we prove the existence theorem of solution for this class of generalized mixed vector equilibrium-like problems.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.429-444
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• 2012

By using Mawhin continuation theorem and comparison theorem, the existence of periodic solution and persistence for a predator-prey system with diffusion and impulses are investigated in this paper. An example and simulation are given to show the effectiveness of the main results.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.869-881
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• 2003

In this paper, a nonautonomous predator-prey dispersion delay models with functional response is studied. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for above models is established.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.577-594
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• 2013

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.299-309
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• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.451-460
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• 2009

We consider the existence of solutions of a nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=f(x, u)$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$. We obtain two new results by linking theorem.