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An application of linking theorem to fourth order elliptic boundary value problem with fully nonlinear term

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주제분류수학

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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.

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.

참고문헌 (11)

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  3. 최규흥, "Nonlinear biharmonic problem with variable coefficient exponential growth term", 한국수학논문집, 18(3), pp.277~288 (2010), 강원경기수학회
  4. T. Jung, "Multiplicity results on a nonlinear biharmonic equation", Nonlinear Anal, 30(8), pp.5083~5092 (1997)
  5. 정택선, "Nontrivial solution for the biharmonic boundary value problem with some nonlinear term", 한국수학논문집, 21(2), pp.117~124 (2013), 강원경기수학회[DOI]
  6. T. Jung, "Fourth order elliptic boundary value problem with nonlinear term decaying at the origin", J. Inequalities and Applications, pp.1~8 (2013)
  7. S. Li, "Periodic solutions of an asymptotically linear wave equation", Nonlinear Anal, 1, pp.211~230 (1993)
  8. J.Q. Liu, "Free vibrations for an asymmetric beam equation", Nonlinear Anal, 51, pp.487~497 (2002)
  9. A. M. Micheletti, "Multiplicity results for a fourth-order semilinear elliptic problem", Nonlinear Anal. TMA, 31(7), pp.895~908 (1998)
  10. P. H. Rabinowitz, "Minimax methods in critical point theory with applications to differential equations", CBMS. Regional conf. Ser. Math., 65 (1986), Amer. Math. Soc.
  11. Tarantello, "A note on a semilinear elliptic problem", Diff. Integ.Equat, 5(3), pp.561~565 (1992)

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