Korean Journal of Mathematics

  • 제20권3호
  • /
  • Pages.361-369
  • /
  • 2012
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

SIX SOLUTIONS FOR THE SEMILINEAR WAVE EQUATION WITH NONLINEARITY CROSSING THREE EIGENVALUES

  • Choi, Q-Heung (Department of Mathematics Education Inha University) ;
  • Jung, Tacksun (Department of Mathematics Kunsan National University)
  • 투고 : 2012.08.14
  • 심사 : 2012.09.15
  • 발행 : 2012.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We get a theorem which shows the existence of at least six solutions for the semilinear wave equation with nonlinearity crossing three eigenvalues. We obtain this result by the variational reduction method and the geometric mapping defined on the finite dimensional subspace. We use a contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three-dimensional subspace with three axes spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one-dimensional subspace.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

참고문헌

  1. Q.H. Choi and T. Jung, An application of a variational reduction method to a nonlinear wave equation, J. Differential Equations, 117 (1995), 390-410. https://doi.org/10.1006/jdeq.1995.1058
  2. T. Jung and Q.H. Choi, An application of category theory to the nonlinear wave equation with jumping nonlinearity, Honam Mathematical Journal, 26 (4) (2004), 589-608.
  3. Q.H. Choi and T. Jung, Multiple periodic solutions of a semilinear wave equation at double external resonances, Commun. Appl. Anal. 3 (1) (1999), 73-84.
  4. Q.H. Choi and T. Jung, Multiplicity results for nonlinear wave equations with nonlinearities crossing eigenvalues, Hokkaido Math. J. 24 (1) (1995), 53-62. https://doi.org/10.14492/hokmj/1380892535
  5. A.C. Lazer and P.J. McKenna, Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems, J. Math. Anal. Appl. 107 (1985), 371-395. https://doi.org/10.1016/0022-247X(85)90320-8
  6. A.C. Lazer and P.J. McKenna, Global bifurcation and a theorem of Tarantello, J. Math. Anal. Appl, 181 (1994), 648-655. https://doi.org/10.1006/jmaa.1994.1049
  7. P.J. McKenna and W. Walter, Nonlinear oscillations in a suspension bridge, Arch. Ration. Mech. Anal. 98 (2) (1987), 167-177.
  8. P.J. McKenna and W. Walter, On the multiplicity of the solution set of some nonlinear boundary value problems, Nonlinear Anal. 8 (8) (1984), 893-901. https://doi.org/10.1016/0362-546X(84)90110-X