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- W2619643307 abstract "In this paper, we study the existence of multiple positive solutions of the following Schrödinger-Poisson system with critical exponent $begin{equation*}begin{cases}-Δ u-l(x)φ u=λ h(x)|u|^{q-2}u+|u|^{4}u, text{in} mathbb{R}^{3}, -Δφ=l(x)u^{2}, text{in} mathbb{R}^{3},end{cases}end{equation*}$ where $1 < q < 2 $ and $λ>0 $. Under some appropriate conditions on $ l$ and $h $, we show that there exists $λ^{*}>0 $ such that the above problem has at least two positive solutions for each $λ∈(0,λ^{*}) $ by using the Mountain Pass Theorem and Ekeland's Variational Principle." @default.
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- W2619643307 date "2017-01-01" @default.
- W2619643307 modified "2023-09-27" @default.
- W2619643307 title "Multiple positive solutions for Schrödinger-Poisson system in $mathbb{R}^{3}$ involving concave-convex nonlinearities with critical exponent" @default.
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- W2619643307 doi "https://doi.org/10.3934/cpaa.2017076" @default.
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