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On the Semilinear Elliptic Problems Involving the Critical Sobolev Exponents

Author: AnZhi
Tutor: KangDongSheng
School: Central South University for Nationalities
Course: Applied Mathematics
Keywords: Elliptic Problems Critical exponent Positive solution Changing solutions Asymptotic behavior
CLC: O175.25
Type: Master's thesis
Year: 2010
Downloads: 7
Quote: 0
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Abstract


This paper studies the following semi - linear elliptic equations : omega ? RN ( N ≥ 3 ) is a smooth bounded domain a_i of ∈ omega ( i = 1,2 , .. , k ) of the same for the best Hardy constant 2 * = 2N / ( N - 2 ) critical Sobolev Exponent . Firstly, local Palais - Smale condition , and then use the variational principle and the Mountain Pass Theorem to prove one with Critical Sobolev Exponent and Hardy semilinear elliptic equations changing solutions for the existence and use of the the Moser iterative method to prove non- trivial solution of the equation in the asymptotic properties of the singular point .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Elliptic equations
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