• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1541-1547
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• 2011

In this paper, using B.Ricceri's three critical points theorem, we prove the existence of at least three classical solutions for the problem $$\{u^{(4)}(t)={\lambda}f(t,\;u(t)),\;t{\in}(0,\;1),\\u(0)=u(1)=u^{\prime}(0)=u^{\prime}(1)=0,$$ under appropriate hypotheses.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.483-497
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• 2010

In this paper we study some qualitative behavior of the solutions of the difference equation $x_{n+1}=ax_n=\frac{bx_n}{cx_n-dx_{n-1}}$, n=0,1,$\ldots$, where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants with $cx_0-dx_{-1}\neq0$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.513-524
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• 2015

Here, we show that the title equation has no positive integer solutions (m, n), where ${\phi}$ is the Euler function.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.281-290
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• 2009

The famous Guo-Krasnosel'skii fixed point theorems concerning cone expansion and compression of norm type and order type are extended, respectively. As an application, the existence of multiple positive solutions for systems of Hammerstein type integral equations is considered.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.175-186
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• 2018

Let (M, J, ${\theta}$) be a complete pseudohermintian (2n+1)-manifold. In this paper, we derive the subgradient estimate for positive solutions to a nonlinear subelliptic equation ${\Delta}_bu+au{\log}u+bu=0$ on M, where $a{\leq}0$, b are two real constants.

• Nuclear Engineering and Technology
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• v.5 no.2
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• pp.132-136
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• 1973

Uniformly irradiated parallel-plate ionization chamber filled with a gas free of negative ion-forming contaminants was studied. Computer solutions for the electric field and the positive and negative charge densities at various degrees of saturation were obtained and discussed.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.479-483
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• 2006

For any fixed $\lambda\leq-\frac{1}{2}$, there exists $f(\eta){\in}C^1[0,+\infty)$ which satisfies the following nonlinear boundary value problem f'+ff'+$\lambda(l-f'^2)=0$ a.e.in $(0,+\infty)$, f(0)=0, f'(0) = 0, $f'(+\infty)=1$, which arises in boundary layer theory in fluid mechanics.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.879-889
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• 2011

In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.19-26
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• 1989

We in this paper have defined the concept of .epsilon.-symmetric relation between the Lagrangean relaxation and the Benders' decomposition. This links the solutions of the Lagrangean subproblems and those of the Benders' subproblems even under positive duality gaps. As an application we have discussed the reduction of the size for a special class of problems.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.313-329
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• 2020

In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.