ON QUASILINEAR BREZIS-NIRENBERG TYPE PROBLEMS WITH WEIGHTS
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Date
2010
Journal Title
Journal ISSN
Volume Title
Publisher
KHAYYAM PUBL CO INC
Abstract
In this paper we study Brezis-Nirenberg type results for radial solutions of a qumilinear elliptic equation of the form
{-Delta(p)u = lambda C(vertical bar x)vertical bar u vertical bar(p-2) u + B(vertical bar x vertical bar)vertical bar u vertical bar(q-2)u, a.e. x is an element of B-R(0) subset of R-N, R > 0, u = 0, on partial derivative B-R(0),
where lambda is an element of R, q >= p > 1, Delta(p)u = div(vertical bar del(u)vertical bar(p-2)del u), B-R(0) denotes the ball of radius R > 0 centered at 0 in R-N, and the weights B, C are appropriate positive measurable radially symmetric functions.
{-Delta(p)u = lambda C(vertical bar x)vertical bar u vertical bar(p-2) u + B(vertical bar x vertical bar)vertical bar u vertical bar(q-2)u, a.e. x is an element of B-R(0) subset of R-N, R > 0, u = 0, on partial derivative B-R(0),
where lambda is an element of R, q >= p > 1, Delta(p)u = div(vertical bar del(u)vertical bar(p-2)del u), B-R(0) denotes the ball of radius R > 0 centered at 0 in R-N, and the weights B, C are appropriate positive measurable radially symmetric functions.
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Keywords
CRITICAL SOBOLEV, EQUATIONS, EIGENVALUE, EXISTENCE