一类半线性椭圆问题多解的存在性

Existence of Multiple Solutions for a Class of Semilinear Elliptic Problems

利用了3个临界点定理,研究了一类半线性椭圆方程:-△u+a(x)u=f(x,u),x∈Ω,在H_0~1(Ω)中至少存在两个非平凡解,其中Ω为R^N中的光滑有界区域,N≥3,a(x)>0,并且满足a(x)∈L^(N/2)(Ω).

Using three critical points theorem, we show that the semilinear elliptic equation -△u＋ a （x）u = f（x,u）, x ∈Ω, possesses at least two nontrivial solutions in H0^1 （Ω）, where Ω is a hounded smooth domain in R^N, N ≥3 ,a （x）〉0 and satisfies a（x）∈L^N/2（Ω）.