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This paper is concerned with the existence of positive solutions of the following Dirichlet problem for p-mean curvature operator with critical exponent: -div((1 |▽u|~2)(p-2)/2▽u)=λu~(p*-1) μu~(q-1),u>0,x∈Ω, u=0,x∈■Ω, where u∈W_0~(1,p)(Ω),Ωis a bounded domain in R~N(N>p>1)with smooth boundary ■Ω,2<=p<=q<=P~*,P~*=(Np)/(N-p),λ,P>0.It reaches the conclusions that this problem has at least one positive solution in the different cases.It is discussed the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with critical exponent by using Nehari-type duality property firstly.As p=2,q=p,the result is correspond to that of Laplace operator. 相似文献
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纳税信誉等级评定模型 总被引:2,自引:1,他引:1
首先构建了用于评价分析的递阶层次系统 ,然后介绍模糊决策理论及灰色系统理论在数据处理方面的应用 ,最后用两种不同的方法对模拟数据进行了分析 ,得到了企业的综合评分 . 相似文献
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This paper is concerned with the following nonlinear Dirichlet problem:{-Δpu=|u|^p*-2 u λf(x,u) x∈Ω;u=0 x∈эΩ} whereΔp^u = div(|∧u|^p-2∧u) is the p-Laplacian of u,Ω is a bounded in R^n(n≥3),1<p<n, p=pn/n-p is the critical exponent for the Sobolev imbedding,λ>0 and f(x,u)satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p=2 or f(x,u) = |u|^q-2 u, where 1<q<p, are generalized. 相似文献
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