一类p(x)-Laplace方程径向正解的奇异性

Singularity of Positive Radial Solutions for a Class of p(x)-Laplacian Equations

给出了一类 p(x) -

The singularity of pos it ive radial solutions is studied in a neighborhood of zero for p(x) Laplacia n equations-Δ p(x)u=-div(｜u｜ p(x)-2u)=f(x,u),on the condition that p(x) and f(x,u) are radial about x, where f( x,u)∈C([0,R]×R +,R +) . It is proved that the positive radial solutions o f this equation are singular or regular if the growth speed of f(x,·) is le ss than N(p(x)-1)N-p(x) when u→∞. In additi on, the existence of singular solutions is obtained.