Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth

Quanqing Li, Kaimin Teng and Xian Wu

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: We study the following generalized quasilinear Schrödinger equations with critical growth -divg2u∇u+gug′u∇u|2+Vxu=λfx,u+guGu|2⁎-2Gu,x∈RN, where λ > 0, N ≥ 3, g(s):R→R+ is a C1 even function, g(0) = 1, and g′(s) ≥ 0 for all s ≥ 0, where G(u)≔∫0ug(t)dt. Under some suitable conditions, we prove that the equation has a nontrivial solution by variational method.

Date: 2018
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https://doi.org/10.1155/2018/3615085

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:3615085

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