Elliptic problem with a variable coefficient and a jumping semilinear term
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We obtain the multiple solutions for the fourth order elliptic problem with a variable coefficient and a jumping semilinear term. We have a result that there exist at least two solutions if the variable coefficient of the semilinear term crosses some number of the eigenvalues of the biharmonic eigenvalue problem. We obtain this multiplicity result by applying the Leray-Schauder degree theory.
Abstract
We obtain the multiple solutions for the fourth order elliptic problem with a variable coefficient and a jumping semilinear term. We have a result that there exist at least two solutions if the variable coefficient of the semilinear term crosses some number of the eigenvalues of the biharmonic eigenvalue problem. We obtain this multiplicity result by applying the Leray-Schauder degree theory.
참고문헌 (9)
- Q.H. Choi, "Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation", Acta Math. Sci, 19(4), pp.361~374 (1999)
- Q.H. Choi, "Multiplicity results on nonlinear biharmonic operator", Rocky Mountain J. Math, 29(1), pp.141~164 (1999)
- T.S. Jung, "Multiplicity results on a nonlinear biharmonic equation", Nonlinear Anal, 30(8), pp.5083~5092 (1997)
- 정택선, "On the existence of the third solution of the nonlinear biharmonic equation with dirihlet boundary condition", 충청수학회지, 20(1), pp.81~94 (2007), 충청수학회
- A.C. Lazer, "Multiplicity results for a class of semilinear el- liptic and parabolic boundary value problems", J. Math. Anal. Appl, 107, pp.371~395 (1985)
- P.J. McKenna, "On the multiplicity of the solution set of some nonlinear boundary value problems", Nonlinear Anal, 8, pp.893~907 (1984)
- P.J. McKenna, "On the multiplicity of the solution set of some nonlinear boundary value problems-II", Nonlinear Anal, 10(8), pp.805~812 (1986)
- A.M. Micheletti, "Three solutions of a 4th order elliptic problem via variational theorems of mixed type", Appl. Anal, 75, pp.43~59 (2000)
- Tarantello, "A note on a semilinear elliptic problem", Differential Integral Equations, 5(3), pp.561~565 (1992)