Infinitely many solutions to quasilinear Schrödinger equations with critical exponent

Wang, Li and Wang, Jixiu and Li, Xiongzheng: Infinitely many solutions to quasilinear Schrödinger equations with critical exponent. Electronic journal of qualitative theory of differential equations 5. pp. 1-16. (2019)

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Abstract

This paper is concerned with the following quasilinear Schrödinger equations with critical exponent: −∆pu + V(x)|u| p−2u − ∆p(|u| 2ω)|u| 2ω−2u = ak(x)|u| q−2u + b|u| 2ωp ∗−2u, x ∈ R N. Here ∆pu = div(|∇u| p−2∇u) is the p-Laplacian operator with 1 < p < N, p N p N−p is the critical Sobolev exponent. 1 ≤ 2ω < q < 2ωp, a and b are suitable positive parameters, V ∈ C(RN, [0, ∞)), k ∈ C(RN, R). With the help of the concentration-compactness principle and R. Kajikiya’s new version of symmetric Mountain Pass Lemma, we obtain infinitely many solutions which tend to zero under mild assumptions on V and k.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 5
Page Range: pp. 1-16
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.5
Uncontrolled Keywords: Schrödinger egyenlet
Additional Information: Bibliogr.: p. 14-16. ; összefoglalás angol nyelven
Date Deposited: 2019. May. 31. 07:15
Last Modified: 2019. May. 31. 07:15
URI: http://acta.bibl.u-szeged.hu/id/eprint/58112

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