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A Variational Approach to Discontinuous Problems with Critical Sobolev Exponents

✍ Scribed by C.O. Alves; Ana Maria Bertone; J.V. Goncalves

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
177 KB
Volume
265
Category
Article
ISSN
0022-247X

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✦ Synopsis

We employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form -u = λh x H u -a u q + u 2 * -1 in R N , where λ, a > 0 are parameters, h x is both nonnegative and integrable on R N , H is the Heaviside function, 2 * is the critical Sobolev exponent, and 0 ≤ q < 2 * -1. We obtain existence, multiplicity and regularity of solutions by distinguishing the cases 0 ≤ q ≤ 1 and 1 < q < 2 * -1.

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