Un résultat de non-existence de solution positive pour une équation elliptique. (A nonexistence result for positive solutions of an elliptic equation). (French) Zbl 0719.35028
The paper deals with the equation \(-\Delta u(x)=f(u(x))=\lambda g(x)\) in a bounded n-dimensional domain with Dirichlet boundary conditions under suitable restrictions for f and g. The author proves that for \(\lambda\) large enough the above problem has no positive solutions. To prove this result variational methods are used.
Reviewer: J.Madjarova (Sofia)
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |
| 35J20 | Variational methods for second-order elliptic equations |
References:
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