Multiple positive solutions for a quasilinear elliptic problem involving critical Sobolev–Hardy exponents and concave–convex nonlinearities
✍ Scribed by Tsing-San Hsu
- Book ID
- 108216722
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 264 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0362-546X
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📜 SIMILAR VOLUMES
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.
The main results of this paper establish, via the variational method, the multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents under the presence of symmetry. The concentration-compactness principle allows to prove that the Palais-Smale condition is satisf
Let ⊂ R N be a smooth bounded domain such that 0 ∈ , N 3, 0 s < 2, 2 \* (s) := 2(N - s)/N -2 is the critical Sobolev-Hardy exponent, f (x) is a given function. By using the Ekeland's variational principle and the mountain pass lemma, we prove the existence of multiple solutions for the singular crit
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