Browse > Article
http://dx.doi.org/10.11568/kjm.2014.22.2.355

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)
Publication Information
Korean Journal of Mathematics / v.22, no.2, 2014 , pp. 355-365 More about this Journal
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
Fourth order elliptic boundary value problem; nonlinear term; linking theorem; $(P.S.)_c$ condition;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Tarantello, A note on a semilinear elliptic problem, Diff. Integ.Equat. 5 (3) (1992), 561-565.
2 Q. H. Choi and T. Jung, Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29 (1) (1999), 141-164.   DOI   ScienceOn
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.   DOI   ScienceOn
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).   과학기술학회마을   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
9 A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal. TMA, 31 (7) (1998), 895-908.   DOI   ScienceOn
10 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.
11 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).