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- W2419366912 abstract "In this paper, we are concerned with existence and asymptotic behavior of ground state in the whole space $mathbb{R}^3$ for quasilinear Schrodinger--Poisson systems $$ begin{cases} -Delta u+u+K(x)phi(x)u=a(x)f(u), xin mathbb{R}^3, -mbox{div}[(1+varepsilon^4|nablaphi|^2)nablaphi]=K(x)u^2, xin mathbb{R}^3, end{cases} $$ when the nonlinearity coefficient $varepsilonge 0$ goes to zero, where $f(t)$ is asymptotically linear with respect to $t$ at infinity. Under appropriate assumptions on $K$, $a$ and $ f$, we establish existence of a ground state solution $(u_varepsilon, phi_{varepsilon, K}(u_varepsilon))$ of the above system. Furthermore, for all $varepsilon$ sufficiently small, we show that $(u_varepsilon, phi_{varepsilon, K}(u_varepsilon))$ converges to $(u_0, phi_{0, K}(u_0))$ which is the solution of the corresponding system for $varepsilon=0$." @default.
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- W2419366912 date "2016-01-01" @default.
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- W2419366912 title "Existence and asymptotic behaviour of ground state solutions for quasilinear Schrodinger-Poisson systems in $R^3$" @default.
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- W2419366912 doi "https://doi.org/10.12775/tmna.2016.004" @default.
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