Korean Journal of Mathematics

  • 제17권3호
  • /
  • Pages.299-314
  • /
  • 2009
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  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

CRITICAL POINT THEORY AND AN ASYMMETRIC BEAM EQUATION WITH TWO JUMPING NONLINEAR TERMS

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • 투고 : 2009.08.14
  • 발행 : 2009.06.30
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초록

We investigate the multiple nontrivial solutions of the asymmetric beam equation $u_{tt}+u_{xxxx}=b_1[{(u + 2)}^+-2]+b_2[{(u + 3)}^+-3]$ with Dirichlet boundary condition and periodic condition on t. We reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions of the equation.

키워드

과제정보

연구 과제 주관 기관 : Korea Research Foundation

참고문헌

  1. H. Amann, Saddle points and multiple solutions of differential equation, Math.Z.(1979), 27-166.
  2. A. Ambrosetti and P. H. Rabinowitz, Dual variation methods in critical point theory and applications, J. Functional analysis, 14(1973), 349-381. https://doi.org/10.1016/0022-1236(73)90051-7
  3. Q. H. Choi, T. Jung and P. J. McKenna, The study of a nonlinear suspension bridge equation by a variational reduction mehtod, Appl. Anal., 50(1993),73-92. https://doi.org/10.1080/00036819308840185
  4. 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
  5. A. C. Lazer and P. J. McKenna, A symmetry theorem and applications to non- linear partial differential equations, J. Differential Equations 72(1988), 95-106. https://doi.org/10.1016/0022-0396(88)90150-7
  6. A. C. Lazer and P. J. McKenna, Large-amplitude periodic oscillations in sus- pension bridges: some new connections with nonlinear analysis, SIAM Review, 32(1990), 537-578. https://doi.org/10.1137/1032120
  7. 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
  8. A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Analysis TMA, 31(1998), 895-908. https://doi.org/10.1016/S0362-546X(97)00446-X
  9. A. M. Micheletti, A. Pistoia, Nontrivial solutions for some fourth order semi- linear elliptic problems, Nonlinear Analysis, 34(1998), 509-523. https://doi.org/10.1016/S0362-546X(97)00596-8
  10. Paul H. Rabinobitz, Minimax methods in critical point theory with applications to differential equations, emMathematical Science regional conference series, No. 65, AMS (1984).
  11. G. Tarantello, A note on a semilinear elliptic problem, Diff. Integ. Equations. 5(3)(1992), 561-565.