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NONLINEAR BIHARMONIC PROBLEM WITH VARIABLE COEFFICIENT EXPONENTIAL GROWTH TERM  

Choi, Q-Heung (Department of Mathematics Education Inha University)
Jung, Tacksun (Department of Mathematics Kunsan National University)
Publication Information
Korean Journal of Mathematics / v.18, no.3, 2010 , pp. 277-288 More about this Journal
Abstract
We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.
Keywords
biharmonic boundary value problem; variable coefficient exponential growth term; variational method; generalized mountain pass geometry; 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 Tarantello, A note on a semilinear elliptic problem, Differ. Integral. Equ. Appl. 5(3)(1992), 561-565.
5 Khanfir, S. and Lassoued, L., On the existence of positive solutions of a semi- linear elliptic equation with change of sign, Nonlinear Anal. 22(11)(1994), 1309-1314.   DOI   ScienceOn
6 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
7 Rabinowitz and P. H., Minimax methods in critical point theory with appli- cations to differential equations, CBMS. Regional conf. Ser. Math.65, Amer. Math. Soc., Providence, Rhode Island, 1986.