Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 252, Issue 11, Pages 6133-6162Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2012.02.023
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Funding
- MICINN of Spain [MTM2010-16518, MTM2009-10878, MTM2010-18128, MTM2008-06326-C02-02]
- Comunidad de Madrid-UC3M [CCG10-UC3M/ESP-4609]
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We study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional Laplacian: { (-Delta)alpha/2 = lambda = lambda U-Q + U N+alpha/N-alpha, u > 0 in Omega, u = 0 on (sic)Omega where Omega subset of R-N is a smooth bounded domain, N >= 1, lambda > 0, 0 < q < N+alpha/N-alpha, 0 0, at least one if lambda = Lambda, no solution if lambda > Lambda. For q = 1 we show existence of at least one solution for 0 < lambda < lambda(1) and nonexistence for lambda >= lambda(1). When q > 1 the existence is shown for every lambda > 0. Also we prove that the solutions are bounded and regular. (C) 2012 Elsevier Inc. All rights reserved.
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