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Multiple positive solutions for a critical quasilinear elliptic system with concave–convex nonlinearities

✍ Scribed by Tsing-San Hsu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
629 KB
Volume
71
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we consider a quasilinear elliptic system with both concave-convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.

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✍ Li Wang; Qiaoling Wei; Dongsheng Kang 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 278 KB

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 posi