• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.381-386
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• 1996

We consider the behavior of positive radial solutions (or, briefly, pp.r.s.) of the equation $$ (1.1) ^\Delta u + \lambda f(u) = 0 in\Omega, _u = 0 on \partial\Omega, $$ where $\Omega = {x \in R^n$\mid$A < $\mid$x$\mid$ < B}$ is an annulus in $R^n, n \geq 2, \lambda > 0 and f \geq 0$ is superlinear in u and satisfies f(0) = 0.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1183-1196
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• 2010

Some annulus oscillation criteria are established for the second order damped elliptic differential equation $$\sum\limits_{i,j=1}^N D_i[a_{ij}(x)D_jy]+\sum\limits_{i=1}^Nb_i(x)D_iy+C(x,y)=0$$ under quite general assumption that they are based on the information only on a sequence of annuluses of $\Omega(r_0)$ rather than on the whole exterior domain $\Omega(r_0)$. Our results are extensions of those due to Kong for ordinary differential equations. In particular, the results obtained here can be applied to the extreme case such as ${\int}_{\Omega(r0)}c(x)dx=-\infty$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.331-343
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• 2020

This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems -Δv = λh(x, v) in Ω, v = 0 on ∂Ω, where Ω = {x ∈ R^N : r₁ < |x| < r₂} with 0 < r₁ < r₂, N ≥ 2. The nonlinear term is continuous and satisfies h(x, 0) = h(x, s₁(x)) = h(x, s₂(x)) = 0 for suitable positive, concave function s₁ and negative, convex function s₂, as well as sh(x, s) > 0 for s ∈ ℝ \ {0, s₁(x), s₂(x)}. Moreover, we give the intervals for the parameter λ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.1 no.4
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• pp.305-312
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• 1989

Laminal natural convection heat transfer in the annulus between isothermal horizontal non-circular cylinders is studied by solving the Navier-Stokes and energy equation using an elliptic numerical procedure. Results are obtained to determine the effects of the diameter ratio($D_o/D_i$) and Rayleigh number on heat transfer. The diameter ratio is varied from 1.5 to 13.0 at Pr=0.7, H/L=1.5 and $10^3{\leqslant}Ra_L{\leqslant}4{\times}10^4$. It is found that the diameter ratio causes a more significant on the local heat transfer coefficient of lower semi-circular cylinder and plate than upper semi-circular cylinder. The mean Nusselt number increases as the diameter ratio and Rayleigh number increase, and is higher than that of the circular annulus with a same wetted perimeter.