• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.273-277
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• 2014

In this article, we consider a singular and a degenerate elliptic operators in a divergence form. The singularities exist on a part of boundary, and comparable to the logarithmic distance function or its inverse. If we assume that the operator can be treated in a pointwise sense than distribution sense, with this operator we obtain a priori Harnack continuity near the boundary. In the proof we transform the singular elliptic operator to uniformly bounded elliptic operator with unbounded first order terms. We study this type of estimations considering a De Giorgi conjecture. In his conjecture, he proposed a certain ellipticity condition to guarantee a continuity of a solution.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.355-367
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• 1999

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.155-163
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• 2012

Let E be an elliptic curve over $\mathbb{Q}$. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the $\mathbb{Z}_p$-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.1-10
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• 2009

Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.37-49
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• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.4
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• pp.38-44
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• 2004

The motion response analysis of a submerged elliptic cylinder in waves is presented and the elliptic cylinder is a simplification of the section of submarine in this paper. The method is based on boundary integral method and two-dimensional 3 degree motions are calculated in regular harmonic waves. The fully nonlinear free surface boundary condition is assumed in an numerical domain and this solution is matched along an assumed boundary as a linear solution composed of transient Green function, The large amplitude motions of an elliptic cylinder are directly simulated and effects of wave frequency, wave amplitude and the distance from buoyancy center to gravity center are discussed.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.5
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• pp.37-42
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• 1983

The elliptic functions have transmission zeros on the imaginary axis and exhibit equal ripples in the stopband as well as in the passband. As a consequence they can be made optimal in the sense that the transition band is minimal. However the time domain behaviors turned out to be inferior to those of Chebyshev and Butterworth responses. This paper investigates the unit step responses and impulse responses in order to analyze the effects of various parameters such as passband attenuation, stopband frequencies M. etc., The following are the prominent features. Step responses of elliptic filters rise faster and produce larger overshoots and undershoots with higher natural frequencies. In the case of even functions, the initial values are non-zero which decreases as $\omega$s increases. Unlike Butter-worth or Chebyshev cases the impulse responses start with nonzero valses which also decrease as $\omega$s or order of the function increases. Eight figures are included to illustrate above analysis.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.927-945
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• 2012

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.

• 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.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1285-1301
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• 2018

This paper is devoted to the study of $Tur{\acute{a}}n$-type inequalities for some well-known special functions such as Gauss hypergeometric functions, generalized complete elliptic integrals and confluent hypergeometric functions which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality. We also apply these inequalities for some sample of interest such as incomplete beta function, incomplete gamma function, elliptic integrals and modified Bessel functions to obtain their corresponding $Tur{\acute{a}}n$-type inequalities.