• 제목/요약/키워드: Dirichlet Condition

검색결과 156건 처리시간 0.022초

SOLVABILITY FOR A CLASS OF THE SYSTEM OF THE NONLINEAR SUSPENSION BRIDGE EQUATIONS

  • Jung, Tack-Sun;Choi, Q-Heung
    • 호남수학학술지
    • /
    • 제31권1호
    • /
    • pp.75-85
    • /
    • 2009
  • We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

VARIATIONAL APPROACH AND THE NUMBER OF THE NONTRIVIAL PERIODIC SOLUTIONS FOR A CLASS OF THE SYSTEM OF THE NONTRIVIAL SUSPENSION BRIDGE EQUATIONS

  • Jung, Tack-Sun;Choi, Q-Heung
    • 한국수학교육학회지시리즈B:순수및응용수학
    • /
    • 제16권2호
    • /
    • pp.199-212
    • /
    • 2009
  • We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

  • PDF

STUDY ON THE PERTURBED PIECEWISE LINEAR SUSPENSION BRIDGE EQUATION WITH VARIABLE COEFFICIENT

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
    • /
    • 제19권2호
    • /
    • pp.233-242
    • /
    • 2011
  • We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

Capacitance matrix method for petrov-galerkin procedure

  • Chung, Sei-Young
    • 대한수학회지
    • /
    • 제32권3호
    • /
    • pp.461-470
    • /
    • 1995
  • In this paper a capacitance matrix method is developed for the Poisson equation on a rectangle $$ (1-1) Lu \equiv -(u_{xx} + u_{yy} = f, (x, y) \in \Omega \equiv (0, 1) \times (0, 1) $$ with the homogeneous Dirichlet boundary condition $$ (1-2) u = 0, (x, y) \in \partial\Omega $$ where $\partial\Omega$ is the boundary of the region $\Omega$.

  • PDF

THE SPECTRAL GEOMETRY OF EINSTEIN MANIFOLDS WITH BOUNDARY

  • Park, Jeong-Hyeong
    • 대한수학회지
    • /
    • 제41권5호
    • /
    • pp.875-882
    • /
    • 2004
  • Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

A History of Researches of Jumping Problems in Elliptic Equations

  • Park, Q-Heung;Tacksun Jung
    • 한국수학사학회지
    • /
    • 제15권3호
    • /
    • pp.83-93
    • /
    • 2002
  • We investigate a history of reseahches of a nonlinear elliptic equation with jumping nonlinearity, under Dirichlet boundary condition. The investigation will be focussed on the researches by topological methods. We also add recent researches, relations between multiplicity of solutions and source terms of tile equation when the nonlinearity crosses two eigenvalues and the source term is generated by three eigenfunctions.

  • PDF

NONHOMOGENEOUS DIRICHLET PROBLEM FOR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATIONS WITH SPATIALLY DEPENDENT SECOND ORDER OPERATOR

  • Wang, Qin
    • 대한수학회보
    • /
    • 제53권6호
    • /
    • pp.1597-1612
    • /
    • 2016
  • There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of $Kru{\check{z}}kov^{\prime}s$ doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.

AN APPLICATION OF THE LERAY-SCHAUDER DEGREE THEORY TO THE VARIABLE COEFFICIENT SEMILINEAR BIHARMONIC PROBLEM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
    • /
    • 제19권1호
    • /
    • pp.65-75
    • /
    • 2011
  • We obtain multiplicity results for the nonlinear biharmonic problem with variable coefficient. We prove by the Leray-Schauder degree theory that the nonlinear biharmonic problem has multiple solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions.

ELLIPTIC PROBLEM WITH A VARIABLE COEFFICIENT AND A JUMPING SEMILINEAR TERM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
    • /
    • 제20권1호
    • /
    • pp.125-135
    • /
    • 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.

MULTIPLICITY RESULTS FOR THE WAVE SYSTEM USING THE LINKING THEOREM

  • Nam, Hyewon
    • Korean Journal of Mathematics
    • /
    • 제21권2호
    • /
    • pp.203-212
    • /
    • 2013
  • We investigate the existence of solutions of the one-dimensional wave system $$u_{tt}-u_{xx}+{\mu}g(u+v)=f(u+v)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\v_{tt}-v_{xx}+{\nu}g(u+v)=f(u+v)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ with Dirichlet boundary condition. We find them by applying linking inequlaities.