Forbidden paths and cycles in ordered graphs and matrices期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Forbidden paths and cycles in ordered graphs and matrices

Authors:	János Pach Gábor Tardos

Institution:	(1) Institute of Applied Mathematics, Academy of Mathematics and Systems Science Chinese Academy of Sciences, 100080 Beijing, P. R. of China

Abstract:	Assume $0 \leqslant \mu< \bar \mu = \left( {\frac{{N - 2}}{2}} \right)^2$ % MathType!End!2!1! and let Ω⊂R ^N(N≥4) be a smooth bounded domain, 0∈Ω. We study the semilinear elliptic problem: $- \Delta u - \mu \frac{u}{{\left\| x \right\|^2 }} = \lambda u + Q(x)\left\| u \right\|^{2^* - 2} u,u \in H_0^1 \left( \Omega \right)$ % MathType!End!2!1!. By investigating the effect of the coefficientQ, we establish the existence of nontrivial solutions for any λ>0 and multiple positive solutions with λ,μ>0 small.

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