# Singular Radial Positive Solutions for Nonlinear Elliptic Systems

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We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas, [11].

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In this paper, we study the existence of solutions of nonlinear system involving quasilinear operators -Î”piui = Î»mi (x) nÎ j=1 ujÎ±i,j + âˆ£fi, i = 1, 2, â€¦, n, where the coefficients mi (x) are bounded positive functions, Î» is a positive parameter and fi are given...

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It is shown that the torsion function for an open set D in Euclidean space â„m is in Lâˆž(D) if and only if the spectrum of the Dirichlet Laplacian in D is bounded away from 0. For 1 â‰¤ p â‰¤ âˆž, it is shown that the torsion function for D is in Lp(D) precisely when the...

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We give global estimates on some potential of functions in a bounded domain of the Euclidean space â„n (n â‰¥ 2). These functions may be singular near the boundary and are globally comparable to a product of a power of the distance to the boundary by some particularly well behaved...