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- W4386875992 abstract "In the present paper, we study the following Schr{o}dinger-Maxwell equation with combined nonlinearities begin{align*} displaystyle - Delta u+lambda u+ left(|x|^{-1}ast |u|^2right)u =|u|^{p-2}u +mu|u|^{q-2}uquad text{in} mathbb{ R}^3 quad quad text{and}quad quad int_{mathbb{R}^3}|u|^2dx=a^2, end{align*} where $a>0$, $muin mathbb{R}$, $2<qleq frac{10}{3}leq p<6$ with $qneq p$, $ast$ denotes the convolution and $lambdain mathbb{R}$ appears as a Lagrange multiplier. Under some mild assumptions on $a$ and $mu$, we prove some existence, nonexistence and multiplicity of normalized solution to the above equation. Moreover, the asymptotic behavior of normalized solutions is verified as $murightarrow 0$ and $qrightarrow frac{10}{3}$, and the stability/instability of the corresponding standing waves to the related time-dependent problem is also discussed." @default.
- W4386875992 created "2023-09-20" @default.
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- W4386875992 date "2023-09-18" @default.
- W4386875992 modified "2023-09-27" @default.
- W4386875992 title "Prescribed mass standing waves for Schr{o}dinger-Maxwell equations with combined nonlinearities" @default.
- W4386875992 doi "https://doi.org/10.48550/arxiv.2309.09758" @default.
- W4386875992 hasPublicationYear "2023" @default.
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