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Nodal solutions for a quasilinear Schrödinger equation with critical nonlinearity and non-square diffusion

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  • This paper is concerned with a type of quasilinear Schrödinger equations of the form \begin{eqnarray} -\Delta u+V(x)u-p\Delta(|u|^{2p})|u|^{2p-2}u=\lambda|u|^{q-2}u+|u|^{2p2^{*}-2}u, \end{eqnarray} where $\lambda>0, N\ge3, 4p < q < 2p2^*, 2^*=\frac{2N}{N-2}, 1< p < +\infty$. For any given $k \ge 0$, by using a change of variables and Nehari minimization, we obtain a sign-changing minimizer with $k$ nodes.
    Mathematics Subject Classification: 35J20, 35J62, 35Q55.


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