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- W2897728444 abstract "In this paper we consider the quasilinear critical problem ( P λ ) { − Δ p u = λ u q − 1 + u p ⁎ − 1 in Ω u > 0 in Ω u = 0 on ∂ Ω where Ω is a regular bounded domain in R N , N ≥ p 2 , 1 < p < 2 , p ≤ q < p ⁎ , p ⁎ = N p / ( N − p ) , λ > 0 is a parameter. In spite of the lack of C 2 regularity of the energy functional associated to ( P λ ) , we employ new Morse techniques to derive a multiplicity result of solutions. We show that there exists λ ⁎ > 0 such that, for each λ ∈ ( 0 , λ ⁎ ) , either ( P λ ) has P 1 ( Ω ) distinct solutions or there exists a sequence of quasilinear problems approximating ( P λ ) , each of them having at least P 1 ( Ω ) distinct solutions. These results complete those obtained in [23] for the case p ≥ 2 ." @default.
- W2897728444 created "2018-10-26" @default.
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- W2897728444 date "2019-04-01" @default.
- W2897728444 modified "2023-10-18" @default.
- W2897728444 title "The Brezis–Nirenberg type problem for the p-laplacian (1 < p < 2): Multiple positive solutions" @default.
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- W2897728444 doi "https://doi.org/10.1016/j.jde.2018.10.004" @default.
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