Korean J. Math. Vol. 21 No. 4 (2013) pp.483-493
DOI: https://doi.org/10.11568/kjm.2013.21.4.483

Singular potential biharmonic problem

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Published: Dec 19, 2013
Mathematics Subject Classification:
35J48

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Tacksun Jung
Kunsan National University
Q-Heung Choi
Inha University

Abstract

We investigate the multiplicity of the solutions for a class of the system of the biharmonic equations with some singular potential nonlinearity. We obtain a theorem which shows the existence of the nontrivial weak solution for a class of the system of the biharmonic equations with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and the generalized mountain pass theorem.


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Supporting Agencies

This work was supported by Inha University Research Grant.

References

[1] K.C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkh ̈auser, (1993). Google Scholar

[2] Q. H. Choi and T. Jung, Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation, Acta Math. Sin. 19 (4) (1999), 361–374. Google Scholar

[3] Q. H. Choi and T. Jung, Multiplicity results on nonlinear biharmonic operator, Rocky Mountain J. Math. 29 (1) (1999), 141–164. Google Scholar

[4] T. Jung and Q. H. Choi, Nonlinear biharmonic problem with variable coefficient exponential growth term, Korean J. Math. 18 (3) (2010), 1–12. Google Scholar

[5] T. Jung and Q. H. Choi, Multiplicity results on a nonlinear biharmonic equation, Nonlinear Anal. 30 (8) (1997), 5083–5092. Google Scholar

[6] 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). Google Scholar

[7] A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semi linear elliptic problem, Nonlinear Anal. 31 (7) (1998), 895–908. Google Scholar

[8] P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math. 65, Amer. Math. Soc., Providence, Rhode Island (1986). Google Scholar

[9] Tarantello, A note on a semilinear elliptic problem, Differential Integral Equations 5 (3) (1992), 561–565 . Google Scholar