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- W4302193022 abstract "We consider the nonlinear stationary Schrodinger equation begin{equation*} -Delta u -lambda u= Q(x)|u|^{p-2}u, qquad text{in }mathbb{R}^N end{equation*} in the case where $N geq 3$, $p$ is a superlinear, subcritical exponent, $Q$ is a bounded, nonnegative and nontrivial weight function with compact support in $mathbb{R}^N$ and $lambda in mathbb{R}$ is a parameter. Under further restrictions either on the exponent $p$ or on the shape of $Q$, we establish the existence of a continuous branch $mathcal{C}$ of nontrivial solutions to this equation which intersects ${lambda } times L^{s}(mathbb{R}^N)$ for every $lambda in (-infty, lambda_Q)$ and $s> frac{2N}{N-1}$. Here $lambda_Q>0$ is an explicit positive constant which only depends on $N$ and $text{diam}(text{supp }Q)$. In particular, the set of values $lambda$ along the branch enters the essential spectrum of the operator $-Delta$." @default.
- W4302193022 created "2022-10-06" @default.
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- W4302193022 date "2016-06-02" @default.
- W4302193022 modified "2023-09-25" @default.
- W4302193022 title "Branch continuation inside the essential spectrum for the nonlinear Schrodinger equation" @default.
- W4302193022 doi "https://doi.org/10.48550/arxiv.1606.00606" @default.
- W4302193022 hasPublicationYear "2016" @default.
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