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Singular potential biharmonic problem

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주제분류수학

초록

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.

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.

참고문헌 (9)

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  2. Q. H. Choi, "Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation", Acta Math. Sin, 19(4), pp.361~374 (1999)
  3. Q. H. Choi, "Multiplicity results on nonlinear biharmonic operator", Rocky Mountain J. Math, 29(1), pp.141~164 (1999)
  4. 최규흥, "Nonlinear biharmonic problem with variable coefficient exponential growth term", 한국수학논문집, 18(3), pp.277~288 (2010), 강원경기수학회
  5. T. Jung, "Multiplicity results on a nonlinear biharmonic equation", Nonlinear Anal, 30(8), pp.5083~5092 (1997)
  6. 정택선, "Nontrivial solution for the biharmonic boundary value problem with some nonlinear term", 한국수학논문집, 21(2), pp.117~124 (2013), 강원경기수학회[DOI]
  7. A. M. Micheletti, "Multiplicity results for a fourth-order semilinear elliptic problem", Nonlinear Anal, 31(7), pp.895~908 (1998)
  8. P. H. Rabinowitz, "Minimax methods in critical point theory with applications to differential equations", CBMS Reg. Conf. Ser. Math. 65, Amer. Math. Soc. (1986)
  9. Tarantello, "A note on a semilinear elliptic problem", Differential Integral Equations, 5(3), pp.561~565 (1992)

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