Applications of topolological methods to the semilinear biharmonic problem with different powers

Tacksun Jung, Q-Heung Choi

Abstract


We prove the existence of multiple solutions for the fourth order nonlinear elliptic problem with fully nonlinear term. Our method is based on the critical point theory; the variation of linking method and category theory.

Keywords


Fourth order elliptic boundary value problem, fully nonlinear

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References


Choi, Q. H., Jung, T., Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Mathematica Scientia, 19, No. 4, 361-374 (1999).

Choi, Q. H., Jung, T., Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29, No. 1, 141-164 (1999).

Hofer, H., On strongly indefinite functionals with applications, Trans. Amer. Math. Soc. 275, 185-214 (1983).

Jung, T. S., Choi, Q. H., Multiplicity results on a nonlinear biharmonic equation, Nonlinear Analysis, Theory, Methods and Applications, 30, No. 8, 5083-5092 (1997).

Jung, T. S., Choi, Q. H., A Variation of Linking for the Semilinear Biharmonic Problem , Preprint.

Li, S., Squlkin, A., Periodic solutions of an asymptotically linear wave equation, Nonlinear Analysis, Theory, Methods and Applications, 1, 211-230, (1993).

Micheletti, A. M., Pistoia, A., ıt Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Analysis, TMA, 31, No. 7, 895-908 (1998).

Tarantello, A note on a semilinear elliptic problem, Diff. Integ. Equat., 5, No. 3, 561-565 (1992).




DOI: http://dx.doi.org/10.11568/kjm.2017.25.3.455

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