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- W3132318323 abstract "We study the following Schrödinger-Poisson-Slater type system: begin{equation}label{eq:0.1} begin{cases} -Delta u + V(x) u + lambdaphi (x) u =|u|^{p-1}u,& xin mathbb{R}^3, -Deltaphi = u^2, quad limlimits_{|x|to +infty}phi (x)=0, end{cases} end{equation} where $lambda> 0$ is a parameter, $pin (1,2)$, $Vin C(mathbb{R}^N,mathbb{R}_0^+)$. If $V$ is a constant, or $p in (2,5)$ with $Vin L^{infty}(mathbb{R}^3)$, the above system has been considered in many papers. In this paper, we are interested in the case: $pin (1,2)$ and $V$ being a coercive potential, i.e., $limlimits_{|x|to +infty} V(x)=infty$. We prove that there exists $lambda_0> 0$ such that system (ref{eq:0.1}) has at least two positive solutions $u^0_lambda$ and $u^1_lambda$ for any $lambda in (0, lambda_0)$. Moreover, $u^0_lambda$ is a ground state (i.e., the least energy solution) which must blow up as $lambda rightarrow 0$. Particularly, when $pin ({11}/{7},2)$ and $lambda> 0$ is small enough, we show that the ground state of (ref{eq:0.1}) must be non-radially symmetric even if $V(x)=V(|x|)$, such as $V(x)=|x|^2$." @default.
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- W3132318323 date "2021-02-20" @default.
- W3132318323 modified "2023-09-25" @default.
- W3132318323 title "Positive solutions for Schrödinger-Poisson-Slater system with coercive potential" @default.
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- W3132318323 doi "https://doi.org/10.12775/tmna.2020.041" @default.
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