TY - JOUR T1 - Uniqueness of the Weak Extremal Solution to Biharmonic Equation with Logarithmically Convex Nonlinearities JO - Journal of Partial Differential Equations VL - 4 SP - 315 EP - 329 PY - 2010 DA - 2010/11 SN - 23 DO - http://doi.org/10.4208/jpde.v23.n4.2 UR - https://global-sci.org/intro/article_detail/jpde/5237.html KW - Biharmonic equation KW - logarithmically convex nonlinearities KW - extremal solution KW - uniqueness AB -

In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal (probably singular) solution to the biharmonic equation Δ^2ω=λg(ω) with Dirichlet boundary condition in the unit ball in R^n, where the source term is logarithmically convex. An example is also given to illustrate that the logarithmical convexity is not a necessary condition to ensure the uniqueness of the extremal solution.