Nonlinear biharmonic equation with polynomial growth nonlinear term
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.
Abstract
We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.
참고문헌 (10)
- Chang, K. C., "In nite dimensional Morse theory and multiple solution problems" (1993), Birkhauser
- Choi, Q. H., "Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation", Acta Mathematica Scientia, 19(4), pp.361~374 (1999)
- Choi, Q. H., "Multiplicity results on nonlinear biharmonic operator", Rocky Mountain J. Math, 29(1), pp.141~164 (1999)
- Choi, Q. H., "An application of a variational reduction method to a nonlinear wave equation", J. Di erential Equations, 7, pp.390~410 (1995)
- Jung, T. S., "Multiplicity results on a nonlinear biharmonic equation", Nonlinear Analysis, Theory, Methods and Applications, 30(8), pp.5083~5092 (1997)
- Khan r, S., "On the existence of positive solutions of a semilin-ear elliptic equation with change of sign", Nonlinear Analysis, 22(11), pp.1309~1314 (1994), TMA
- Lazer, A. C., "Multiplicity results for a class of semilinear elliptic and parabolic boundary value problems", J. Math. Anal. Appl, 107, pp.371~395 (1985)
- Micheletti, A. M., "Multiplicity results for a fourth-order semi-linear elliptic problem", Nonlinear Analysis, 31(7), pp.895~908 (1998), TMA
- Rabinowitz, P. H., "Minimax methods in critical point theory with applications to di erential equations, CBMS", Regional conf. Ser. Math. 65, Amer. Math. Soc. (1986)
- Tarantello, "A note on a semilinear elliptic problem", Di . Integ.Equat., 5(3), pp.561~565 (1992)