Data di Pubblicazione:
2009
Citazione:
On a fourth order elliptic problem with a singular nonlinearity / D. Cassani, J.M. do O', N. Ghoussoub. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 9:1(2009), pp. 177-197.
Abstract:
We study a nonlinear eigenvalue problem for the biharmonic operator, subject to Dirichlet boundary conditions, where the nonlinearity exhibits a singularity.
We prove in the ball the existence of an extremal value of the parameter (pull-in voltage) below which there exists a minimal (classical) solution. In the extremal case we prove the existence of a finite energy solution which is unique even in a very weak sense. Above this critical value there are no solutions of any kind; a characterization of the extremal solution is then derived. Estimates on the pull-in voltage, stability properties of solutions and nonexistence results in the whole space are also established.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Biharmonic operator; Extremal solutions; MEMS devices.; Minimal solutions; Nonlinear eigenvalue problems; Semilinear elliptic equations; Singular nonlinearity
Elenco autori:
D. Cassani, J.M. do O', N. Ghoussoub
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