一类非线性椭圆边值问题解的性态研究

The behavior study of solutions to nonlinear elliptic problem

利用了一类非线性椭圆问题及其解的有关性质,研究了非线性椭圆边值问题Lu的解当λ→∞时的渐进性态,并证明了在一定条件下,该类问题的某些正解当参数λ→∞时以测度收敛 这类椭圆问题为Lu=λf(x,u) x∈Ω,λ>0 (aij(x) u)+c(x)u xj xiu| Ω=0和Lu=-∑ni。

The behavior to solutions to nonlinear elliptic problemsLu=λf(x,u)x∈Ω,λ>0 u|_(Ω)=0 where Lu=-∑ni,j=1x_i(a_(ij)(x)ux_j)+c(x)u is studied.Under certain conditions,it is shown that some positive solutions approach some constants in measure when λ→∞.