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- W1865402809 abstract "We consider the following autonomous Kirchhoff-type equation begin{equation*} -left(a+bint_{mathbb{R}^N}|nabla{u}|^2right)Delta u= f(u),~~~~uin H^1(mathbb{R}^N), end{equation*} where $ageq0,b>0$ are constants and $Ngeq1$. Under general Berestycki-Lions type assumptions on the nonlinearity $f$, we establish the existence results of a ground state and multiple radial solutions for $Ngeq2$, and obtain a nontrivial solution and its uniqueness, up to a translation and up to a sign, for $N=1$. The proofs are mainly based on a rescaling argument, which is specific for the autonomous case, and a new description of the critical values in association with the level sets argument." @default.
- W1865402809 created "2016-06-24" @default.
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- W1865402809 date "2017-04-01" @default.
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- W1865402809 title "An autonomous Kirchhoff-type equation with general nonlinearity in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math>" @default.
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- W1865402809 doi "https://doi.org/10.1016/j.nonrwa.2016.09.003" @default.
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