Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

AN APPLICATION OF LINKING THEOREM TO FOURTH ORDER ELLIPTIC BOUNDARY VALUE PROBLEM WITH FULLY NONLINEAR TERM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2014.04.29
  • Accepted : 2014.06.10
  • Published : 2014.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We show the existence of nontrivial solutions for some fourth order elliptic boundary value problem with fully nonlinear term. We obtain this result by approaching the variational method and using a linking theorem. We also get a uniqueness result.

Keywords

Acknowledgement

Supported by : Inha University

References

  1. Q. H. Choi and T. Jung, Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Math. Sci. 19 (4) (1999), 361-374.
  2. Q. H. Choi and T. Jung, Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29 (1) (1999), 141-164. https://doi.org/10.1216/rmjm/1181071683
  3. T. Jung and Q. H. Choi, Nonlinear biharmonic problem with variable coefficient exponential growth term, Korean J. Math. 18 (3) (2010), 1-12.
  4. T. Jung and Q. H. Choi, Multiplicity results on a nonlinear biharmonic equation, Nonlinear Anal. 30 (8) (1997), 5083-5092. https://doi.org/10.1016/S0362-546X(97)00381-7
  5. T. Jung and Q. H. Choi, Nontrivial solution for the biharmonic boundary value problem with some nonlinear term, Korean J. Math, to be appeared (2013). https://doi.org/10.11568/kjm.2013.21.2.117
  6. T. Jung and Q. H. Choi, Fourth order elliptic boundary value problem with nonlinear term decaying at the origin, J. Inequalities and Applications, 2013 (2013), 1-8. https://doi.org/10.1186/1029-242X-2013-1
  7. S. Li and A, Squlkin, Periodic solutions of an asymptotically linear wave equation. Nonlinear Anal. 1 (1993), 211-230.
  8. J.Q. Liu, Free vibrations for an asymmetric beam equation, Nonlinear Anal. 51 (2002), 487-497. https://doi.org/10.1016/S0362-546X(01)00841-0
  9. A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal. TMA, 31 (7) (1998), 895-908. https://doi.org/10.1016/S0362-546X(97)00446-X
  10. 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).
  11. Tarantello, A note on a semilinear elliptic problem, Diff. Integ.Equat. 5 (3) (1992), 561-565.