Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NONLINEAR BIHARMONIC EQUATION WITH POLYNOMIAL GROWTH NONLINEAR TERM

  • JUNG, TACKSUN (Department of Mathematics Kunsan National University) ;
  • CHOI, Q-HEUNG (Department of Mathematics Education Inha University)
  • Received : 2015.07.12
  • Accepted : 2015.09.02
  • Published : 2015.09.30
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Abstract

We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

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Acknowledgement

Supported by : Kunsan National University

References

  1. Chang, K. C., Infinite dimensional Morse theory and multiple solution problems, Birkhauser, (1993).
  2. Choi, Q. H. and Jung, T., Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Mathematica Scientia 19 (4) (1999), 361-374.
  3. Choi, Q. H. and Jung, T., Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29 (1) (1999), 141-164. https://doi.org/10.1216/rmjm/1181071683
  4. Choi, Q. H. and Jung, T., An application of a variational reduction method to a nonlinear wave equation, J. Differential Equations 7 (1995), 390-410.
  5. Jung, T. S. and Choi, Q. H., Multiplicity results on a nonlinear biharmonic equation, Nonlinear Analysis, Theory, Methods and Applications, 30 (8) (1997), 5083-5092. https://doi.org/10.1016/S0362-546X(97)00381-7
  6. Khanfir, S. and Lassoued, L., On the existence of positive solutions of a semilinear elliptic equation with change of sign, Nonlinear Analysis, TMA, 22, No.11, 1309-1314(1994).
  7. Lazer, A. C. and Mckenna, J. P., 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
  8. Micheletti, A. M. and Pistoia, A., Multiplicity results for a fourth-order semi-linear elliptic problem, Nonlinear Analysis, TMA, 31 (7) (1998), 895-908.
  9. Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations, CBMS. Regional conf. Ser. Math. 65, Amer. Math. Soc., Providence, Rhode Island (1986).
  10. Tarantello, A note on a semilinear elliptic problem, Diff. Integ.Equat., 5 (3) (1992), 561-565.