TY - JOUR
T1 - Uniqueness of the Weak Extremal Solution to Biharmonic Equation with Logarithmically Convex Nonlinearities
AU - Xue Luo 
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 - <p>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.</p>