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- W4386820072 abstract "<abstract><p>In this paper, we devote to studying the existence of normalized solutions for the following Schrödinger equation with Sobolev critical nonlinearities.</p> <p><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{align*} &left{begin{array}{ll} -Delta u = lambda u+mulvert u rvert^{q-2}u+lvert u rvert^{p-2}u&{mbox{in}} mathbb{R}^N, int_{mathbb{R}^N}lvert urvert^2dx = a^2, end{array}right. end{align*} $end{document} </tex-math></disp-formula></p> <p>where $ Ngeqslant 3 $, $ 2 < q < 2+frac{4}{N} $, $ p = 2^* = frac{2N}{N-2} $, $ a, mu > 0 $ and $ lambdainmathbb{R} $ is a Lagrange multiplier. Since the existence result for $ 2+frac{4}{N} < p < 2^* $ has been proved, using an approximation method, that is let $ prightarrow 2^* $, we obtain that there exists a mountain-pass type solution for $ p = 2^* $.</p></abstract>" @default.
- W4386820072 created "2023-09-19" @default.
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- W4386820072 date "2023-01-01" @default.
- W4386820072 modified "2023-10-06" @default.
- W4386820072 title "Existence of normalized solutions for the Schrödinger equation" @default.
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- W4386820072 doi "https://doi.org/10.3934/cam.2023028" @default.
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