Nonlinear biharmonic boundary value problem. (English) Zbl 1302.35145
Summary: We consider the nonlinear biharmonic equation with variable coefficient and polynomial growth nonlinearity and Dirichlet boundary condition. We get two theorems. One theorem says that there exists at least one bounded solution under some condition. The other one says that there exist at least two solutions, one of which is a bounded solution and the other of which has a large norm under some condition. We obtain this result by the variational method, generalized mountain pass geometry and the critical point theory of the associated functional.
MSC:
| 35J20 | Variational methods for second-order elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
biharmonic boundary value problem; polynomial growth; variational method; generalized mountain pass geometry; critical point theory; \((PS)\) conditionReferences:
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