Existence and asymptotical behavior of positive solutions for the Schrödinger-Poisson system with double quasi-linear terms

Peng, Xueqin; Jia, Gao

doi:10.3934/dcdsb.2021134

Cited by 2 publications

(1 citation statement)

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“…Later, Figueiredo and Siciliano 11 extended the bounded domain case to

ℝ^{3}

and proved the existence of solutions for quasilinear Schrödinger–Poisson system. In Peng and Jia, 12 we extended these results in Figueiredo and Siciliano 11 and considered Schrödinger–Poisson system with double quasilinear terms. Note that if

ε = 0

, () becomes the well‐known Schrödinger–Poisson system.…”

Section: Introductionmentioning

confidence: 87%

Quasilinear Schrödinger–Poisson system with exponential and logarithmic nonlinearities

Peng

Jia

Huang

2022

Math Methods in App Sciences

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In this paper, we consider the following quasilinear Schrödinger–Poisson system with exponential and logarithmic nonlinearities −normalΔu+ϕu=false|ufalse|p−2ulogfalse|ufalse|2+λffalse(ufalse),0.30em0.1emin0.51emnormalΩ,−normalΔϕ−ε4normalΔ4ϕ=u2,0.30em0.1emin0.51emnormalΩ,u=ϕ=0,0.30em0.1emon0.51em∂normalΩ, where 40 are parameters, normalΔ4ϕ=divfalse(false|∇ϕfalse|2∇ϕfalse),normalΩ⊂ℝ2 is a bounded domain, and f has exponential critical growth. By adopting the reduction argument and a truncation technique, we prove for every ε>0, the above system admits at least one pair of nonnegative solutions false(uε,λ,ϕε,λfalse) for λ>0 large. Furthermore, we research the asymptotical behavior of solutions with respect to the parameters ε and λ. The novelty of this system is the intersection among the quasilinear term, logarithmic term, and exponential critical term. These results are new and improve some existing results in the literature.

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“…Later, Figueiredo and Siciliano 11 extended the bounded domain case to