二阶椭圆型微分方程解的振动定理

Oscillation Theorems for Elliptic Equations of Second Order

考虑二阶非线性椭圆型微分方程∑ni,j=1 xi[Aij( x,y) xjy]+ q( x) f( y) =0 ,( E)其中 q( x)在外区域 Ω∈Rn 上变号 .利用偏 Riccati变换和积分平均技巧 ,建立了方程 ( E)所有解振动的充分准则 .

Consider the second order elliptic equations ∑ni,j=1 x-i[A-{ij}(x, y)x-jy]+q(x)f(y)=0.(E)Some oscillation criteria are obtained for Eq.(E) in an exterior domain ΩR+n, (n≥2), where q(x) is allowed to change sign.Generalized partial Riccati transformation and averaging technique are employed to establish our results.