We obtain inÿnitely many solutions for the problem where N ¿ 3, 1 ¡ q ¡ p ¡ s. Our result extends those of Tonkes (Topology Methods Nonlinear Anal. 13 (1999) 251) in two aspects: we don't require s 6 p \* , and the requirements on the weight h also be relaxed.
✦ LIBER ✦
Two solutions for an elliptic equation with fast increasing weight and concave–convex nonlinearities
✍ Scribed by Furtado, Marcelo F.; Ruviaro, Ricardo; da Silva, João Pablo P.
- Book ID
- 122110791
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 296 KB
- Volume
- 416
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
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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