Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

EXISTENCE OF MULTIPLE SOLUTIONS OF A SEMILINEAR BIHARMONIC PROBLEM WITH VARIABLE COEFFICIENTS

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2011.02.09
  • Accepted : 2011.03.05
  • Published : 2011.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

We obtain multiplicity results for the biharmonic problem with a variable coefficient semilinear term. We show that there exist at least three solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions. We obtain this multiplicity result by applying the Leray-Schauder degree theory.

Keywords

References

  1. K. C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkhauser, 1993.
  2. Q. H. Choi and T. Jung, Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Mathematica Scientia, 19 (1999), no. 4, 361-374. https://doi.org/10.1016/S0252-9602(17)30519-2
  3. Q. H. Choi and T. Jung, Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29 (1999), no. 1, 141-164. https://doi.org/10.1216/rmjm/1181071683
  4. Q. H. Choi and T. Jung, An application of a variational reduction method to a nonlinear wave equation, J. Differential Equations 7 (1995), 390-410.
  5. T. Jung and Q. H. Choi, Multiplicity results on a nonlinear biharmonic equation, Nonlinear Analysis, Theory, Methods and Applications, 30 (1997), no. 8, 5083-5092. https://doi.org/10.1016/S0362-546X(97)00381-7
  6. A. C. Lazer and P. J. McKenna, 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
  7. P. J. McKenna and W. Walter, On the multiplicity of the solution set of some nonlinear boundary value problems, Nonlinear Analysis, Theory, Methods and Applications, 8 (1984), 893-907. https://doi.org/10.1016/0362-546X(84)90110-X
  8. A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Analysis, TMA, 31 (1998), no. 7, 895-908. https://doi.org/10.1016/S0362-546X(97)00446-X
  9. P. H. Rabinowitz, 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. G. Tarantello, A note on a semilinear elliptic problem, Diff. Integ. Equat. 5 (1992), no. 3, 561-565.