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FOURTH ORDER ELLIPTIC BOUNDARY VALUE PROBLEM WITH SQUARE GROWTH NONLINEARITY  

Jung, Tacksun (Department of Mathematics Kunsan National University)
Choi, Q-Heung (Department of Mathematics Education Inha University)
Publication Information
Korean Journal of Mathematics / v.18, no.3, 2010 , pp. 323-334 More about this Journal
Abstract
We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.
Keywords
fourth order elliptic boundary value problem; square growth nonlinear term; finite dimensional reduction method; variational method; critical point theory; (P.S.) condition;
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1 Choi, Q. H. and Jung, T., Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Math. Sci. 19(4)(1999), 361-374.
2 Choi, Q. H. and Jung, T., Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29(1) (1999), 141-164.   DOI   ScienceOn
3 Jung, T. S. and Choi, Q. H., Multiplicity results on a nonlinear biharmonic equation, Nonlinear Anal. 30(8)(1997), 5083-5092.   DOI   ScienceOn
4 Micheletti, A. M. and Pistoia, A., Multiplicity results for a fourth-order semi- linear elliptic problem, Nonlinear Anal. 31(7)(1998), 895-908.   DOI   ScienceOn
5 Rabinowitz and P. H.,Minimax methods in critical point theory with applica- tions to differential equations, CBMS. Regional conf. Ser. Math. 65, Amer. Math. Soc., Providence, Rhode Island, 1986.
6 Tarantello, A note on a semilinear elliptic problem, Differ. Integral. Equ. Appl. 5(3)(1992), 561-565.