• 제목/요약/키워드: Semilinear Elliptic problem

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ELLIPTIC PROBLEM WITH A VARIABLE COEFFICIENT AND A JUMPING SEMILINEAR TERM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
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    • 제20권1호
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    • pp.125-135
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    • 2012
  • We obtain the multiple solutions for the fourth order elliptic problem with a variable coefficient and a jumping semilinear term. We have a result that there exist at least two solutions if the variable coefficient of the semilinear term crosses some number of the eigenvalues of the biharmonic eigenvalue problem. We obtain this multiplicity result by applying the Leray-Schauder degree theory.

AT LEAST TWO SOLUTIONS FOR THE SEMILINEAR BIHARMONIC BOUNDARY VALUE PROBLEM

  • Jung, Tacksun;Choiy, Q-Heung
    • Korean Journal of Mathematics
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    • 제22권4호
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    • pp.633-644
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    • 2014
  • We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

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

  • Ko, Bong-Soo;Lee, Yong-Hoon
    • 대한수학회지
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    • 제39권3호
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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.

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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LONG TIME BEHAVIOR OF SOLUTIONS TO SEMILINEAR HYPERBOLIC EQUATIONS INVOLVING STRONGLY DEGENERATE ELLIPTIC DIFFERENTIAL OPERATORS

  • Luyen, Duong Trong;Yen, Phung Thi Kim
    • 대한수학회지
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    • 제58권5호
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    • pp.1279-1298
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    • 2021
  • The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

ON A NEUMANN PROBLEM AT RESONANCE FOR NONUNIFORMLY SEMILINEAR ELLIPTIC SYSTEMS IN AN UNBOUNDED DOMAIN WITH NONLINEAR BOUNDARY CONDITION

  • Hoang, Quoc Toan;Bui, Quoc Hung
    • 대한수학회보
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    • 제51권6호
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    • pp.1669-1687
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    • 2014
  • We consider a nonuniformly nonlinear elliptic systems with resonance part and nonlinear Neumann boundary condition on an unbounded domain. Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition.