一类二阶半线性椭圆方程边值问题正解的熄灭现象

The Quenching Phenomenon on the Positive Solutions to Semi Iinear Elliptic Equation

讨论了一类二阶半线性椭圆方程u″(t)+ρ(t)f(u(t))=0的第一类边值问题:u″(t)+ρ(t)f(u(t))=0,u(t0)=u(t1)=0,0<t0<t1<+∞的径向正解的熄灭现象。在假设条件f∈C1(0,+∞),f(t)/tλ在(0,+∞)上非增,λ∈[0,1)下通过变量代换与构造积分等式得到该问题的径向正解出现熄灭现象的充要条件。

The quenching phenomenon on the radial positive solutions to semi linear elliptic equation Δu+f(u)=0 is discussed.By constructing variate transformation and integral identity,the equal condition on the quenching phenomenon of the positive solutions to the first boundary value problem of the semi linear elliptic equation is derived.