• 제목/요약/키워드: Radial solutions

검색결과 193건 처리시간 0.023초

RADIAL OSCILLATION OF LINEAR DIFFERENTIAL EQUATION

  • Wu, Zhaojun
    • 대한수학회보
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    • 제49권5호
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    • pp.911-921
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    • 2012
  • In this paper, the radial oscillation of the solutions of higher order homogeneous linear differential equation $$f^{(k)}+A_{n-2}(z)f^{(k-2)}+{\cdots}+A_1(z)f^{\prime}+A_0(z)f=0$$ with transcendental entire function coefficients is studied. Results are obtained to extend some results in [Z. Wu and D. Sun, Angular distribution of solutions of higher order linear differential equations, J. Korean Math. Soc. 44 (2007), no. 6, 1329-1338].

Exact solutions of the piezoelectric transducer under multi loads

  • Zhang, Taotao;Shi, Zhifei
    • Smart Structures and Systems
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    • 제8권4호
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    • pp.413-431
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    • 2011
  • Under the external shearing stress, the external radial stress and the electric potential simultaneously, the piezoelectric hollow cylinder transducer is studied. With the Airy stress function method, the analytical solutions of this transducer are obtained based on the theory of piezo-elasticity. The solutions are compared with the finite element results of Ansys and a good agreement is found. Inherent properties of this piezoelectric cylinder transducer are presented and discussed. It is very helpful for the design of the bearing controllers.

NODAL SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN ANNULAR DOMAINS

  • Jang, Soon-Yeun;Pahk, Dae-Hyeon
    • 대한수학회지
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    • 제35권2호
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    • pp.387-398
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    • 1998
  • We investigate the existence of radial nodal solutions of the elliptic equation $\Delta$u + h($\mid$x$\mid$)f(u) = 0, in annular domains. It is proved that for each integer k $\geq$ 1, there exist at least one radially symmetric solution which has exactly k nodes.

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Analysis and Control Parameter Estimation of a Tubular Linear Motor with Halbach and Radial Magnet Array

  • Jang Seok-Myeong;Choi Jang-Young;Cho Han-Wook;Lee Sung-Ho
    • KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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    • 제5B권2호
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    • pp.154-161
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    • 2005
  • In the machine tool industry, direct drive linear motor technology is an interesting means to achieve high acceleration, and to increase reliability. This paper analyzes and compares the characteristics of a tubular linear motor with Halbach and radial magnet array, respectively. First, the governing equations are established analytically in terms of the magnetic vector potential and two dimensional cylindrical coordinate systems. Then, we derive magnetic field solutions due to the PMs and the currents. Motor thrust, flux linkage and back emf are also derived. The results are shown to be in good conformity with those obtained from the commonly used finite element method. Finally, control parameters are obtained from analytical solutions.

SINGULAR SOLUTIONS OF AN INHOMOGENEOUS ELLIPTIC EQUATION

  • Bouzelmate, Arij;Gmira, Abdelilah
    • Nonlinear Functional Analysis and Applications
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    • 제26권2호
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    • pp.237-272
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    • 2021
  • The main purpose of the present paper is to study the asymptotic behavior near the origin of radial solutions of the equation 𝚫p u(x) + uq(x) + f(x) = 0 in ℝN\{0}, where p > 2, q > 1, N ≥ 1 and f is a continuous radial function on ℝN\{0}. The study depends strongly of the sign of the function f and the asymptotic behavior near the origin of the function |x|λf(|x|) with suitable conditions on λ > 0.

SYMMETRY OF COMPONENTS FOR RADIAL SOLUTIONS OF γ-LAPLACIAN SYSTEMS

  • Wang, Yun
    • 대한수학회지
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    • 제53권2호
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    • pp.305-313
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    • 2016
  • In this paper, we give several sufficient conditions ensuring that any positive radial solution (u, v) of the following ${\gamma}$-Laplacian systems in the whole space ${\mathbb{R}}^n$ has the components symmetry property $u{\equiv}v$ $$\{\array{-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u,v)\text{ in }{\mathbb{R}}^n,\\-div({\mid}{\nabla}v{\mid}^{{\gamma}-2}{\nabla}v)=g(u,v)\text{ in }{\mathbb{R}}^n.}$$ Here n > ${\gamma}$, ${\gamma}$ > 1. Thus, the systems will be reduced to a single ${\gamma}$-Laplacian equation: $$-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u)\text{ in }{\mathbb{R}}^n$$. Our proofs are based on suitable comparation principle arguments, combined with properties of radial solutions.

RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS IN $R^n$

  • Naito, Yuki
    • 대한수학회지
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    • 제37권5호
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    • pp.751-761
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    • 2000
  • Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.

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PROPERTIES OF POSITIVE SOLUTIONS FOR THE FRACTIONAL LAPLACIAN SYSTEMS WITH POSITIVE-NEGATIVE MIXED POWERS

  • Zhongxue Lu;Mengjia Niu;Yuanyuan Shen;Anjie Yuan
    • 대한수학회지
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    • 제61권3호
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    • pp.445-459
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    • 2024
  • In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give two special cases.

NODAL SOLUTIONS FOR AN ELLIPTIC EQUATION IN AN ANNULUS WITHOUT THE SIGNUM CONDITION

  • Chen, Tianlan;Lu, Yanqiong;Ma, Ruyun
    • 대한수학회보
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    • 제57권2호
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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 ∈ RN : 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.

A Nonlinear Elliptic Equation of Emden Fowler Type with Convection Term

  • Mohamed El Hathout;Hikmat El Baghouri;Arij Bouzelmate
    • Kyungpook Mathematical Journal
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    • 제64권1호
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    • pp.113-131
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    • 2024
  • In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆p u + 𝛼|u|q-1u + 𝛽x.∇(|u|q-1u) = 0 for x ∈ ℝN, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.