An Existence Result for a Generalized Quasilinear Schrödinger Equation with Nonlocal Term

In this paper, we consider the following generalized quasilinear Schrödinger equation with nonlocal term −divg2u∇u+gug′u∇u2+Vxu=λx−μ∗upup−2u,x∈ℝN, where N≥3, g:ℝ→ℝ+ is a C1 even function, g0=1, g′s≥0 is for all s≥0, lim∣s∣→+∞gs/sα−1≔β>0 is for some α>1, and α−1gs≥g′ss is for all s≥0, 2α≤p≤2αN−...

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Published in:Journal of function spaces 2020, Vol.2020 (2020), p.1-6
Main Authors: Nie, Jianjun, Zhang, Jian, Teng, Kaimin, Li, Quanqing
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Inequality
Schrodinger equation
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description In this paper, we consider the following generalized quasilinear Schrödinger equation with nonlocal term −divg2u∇u+gug′u∇u2+Vxu=λx−μ∗upup−2u,x∈ℝN, where N≥3, g:ℝ→ℝ+ is a C1 even function, g0=1, g′s≥0 is for all s≥0, lim∣s∣→+∞gs/sα−1≔β>0 is for some α>1, and α−1gs≥g′ss is for all s≥0, 2α≤p≤2αN−μ/N−2, and 0
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subjects Inequality
Schrodinger equation
title An Existence Result for a Generalized Quasilinear Schrödinger Equation with Nonlocal Term
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