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Multiple positive solutions for -Laplace elliptic equations involving concave–convex nonlinearities and a Hardy-type term

✍ Scribed by Li Wang; Qiaoling Wei; Dongsheng Kang

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 278 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.09.017

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✦ Synopsis

where Ω ⊂ R N is a bounded domain such that 0 ∈ Ω, 1 < q < p, λ > 0, µ < μ, f and g are nonnegative functions, μ = ( N-p p ) p is the best Hardy constant and p * = Np N-p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple positive solutions to this equation is verified.

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