• Title/Summary/Keyword: Radial solutions

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ON RADIAL OSCILLATION OF ENTIRE SOLUTIONS TO NONHOMOGENEOUS ALGEBRAIC DIFFERENTIAL EQUATIONS

  • Zhang, Guowei
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.545-559
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    • 2018
  • In this paper we mainly investigate the properties of the solutions to a type of nonhomogeneous algebraic differential equation in an angular domain. It includes the Borel directions of the solutions, the width of angular domains in which the solutions take its order and the measure of radial distributions of Julia sets of the solutions.

EXISTENCE OF THE THIRD POSITIVE RADIAL SOLUTION OF A SEMILINEAR ELLIPTIC PROBLEM ON AN UNBOUNDED DOMAIN

  • Ko, Bong-Soo;Lee, Yong-Hoon
    • Journal of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.439-460
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    • 2002
  • We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

NONRELATIVISTIC LIMIT IN THE SELF-DUAL ABELIAN CHERN-SIMONS MODEL

  • Han, Jong-Min;Song, Kyung-Woo
    • Journal of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.997-1012
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    • 2007
  • We consider the nonrelativistic limit in the self-dual Abelian Chern-Simons model, and give a rigorous proof of the limit for the radial solutions to the self-dual equations with the nontopological boundary condition when there is only one-vortex point. By keeping the shooting constant of radial solutions to be fixed, we establish the convergence of radial solutions in the nonrelativistic limit.

RADIAL SYMMETRY AND SPHERICAL NODAL SET OF SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS

  • Seok, Yong-Jing
    • Communications of the Korean Mathematical Society
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    • v.10 no.1
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    • pp.133-135
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    • 1995
  • In this note, we will investigate the radial symmetry of some kind of solutions of nonlinear ellipitic equations $$ \Delta U = f(U) $$ $$ (1.1) U = 0 in B $$ $$ U \in C^2 (\bar{B}) on \partial B$$ Here f is $C^1$ and B denotes a n-dimensional unit ball in $R^n$.

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THE GLOBAL EXISTENCE AND BEHAVIOR OF RADIAL SOLUTIONS OF A NONLINEAR p-LAPLACIAN TYPE EQUATION WITH SINGULAR COEFFICIENTS

  • Hikmat El Baghouri;Arij Bouzelmate
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.2
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    • pp.333-360
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    • 2024
  • This paper is concerned with the radial solutions of a nonlinear elliptic equation ∆pu + |x|𝑙1 |u|q1-1 u + |x|𝑙2 |u|q2-1 u = 0, x ∈ ℝN, where p > 2, N ≥ 1, q2 > q1 ≥ 1, -p < 𝑙2 < 𝑙1 ≤ 0 and -N < 𝑙2 < 𝑙1 ≤ 0. We prove the existence of global solutions, we give their classification and we present the explicit behavior of positive solutions near the origin and infinity.

POSITIVE RADIAL SOLUTIONS OF $DELTA U + LAMBDA F(U) 0$ ON ANNULUS

  • Bae, Soo-Hyun;Park, Sang-Don;Pahk, Dae-Hyeon
    • 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.

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