R^N 上非齐次非线性椭圆型方程的多解性

Multicity of Solutions for Nonhomogeneous Nonlinear Elliptic Equations in R N

讨论了问题－△ｕ＋μｕ＝Ｑ（ｘ）｜ｕ｜ｐ－２ｕ＋ｆ（ｘ），ｕ∈Ｈ１（ＲＮ）的正解和变号解的存在性，这里Ｎ≥３，２＜ｐ＜２Ｎ／（Ｎ－２），μ＞０，Ｑ（ｘ）∈Ｃ（ＲＮ），且０ｆ≥０．

The existence of positive and nodal solutions for the following problem -Δu+μu=Q(x)|u| p-2 u+f(x), u∈H 1(R N), where N≥3,2<p<2N/(N-2),μ>0,Q(x)∈C(R N),and 0f>0.are considered