Schrödinger equation with multiparticle potential and critical nonlinearity
Keywords
Schrödinger equation, multiparticle potential, Hardy inequality, ground state, concentration-compactnessAbstract
We study the existence and non-existence of ground states for the Schrödinger equations $-\Delta u -\lambda\sum_{i< j}u/|x_i-x_j|^2 = |u|^{2^*-2}u$, $x=(x_1,\ldots,x_m)\in {\mathbb R}^{mN}$, and $-\Delta u -\lambda u/|y|^2 = |u|^{2^*-2}u,\quad x=(y,z)\in {\mathbb R}^N$. In both cases we assume $\lambda\ne 0$ and $\lambda< \overline\lambda$, where $\overline\lambda$ is the Hardy constant corresponding to the problem.Downloads
Published
2009-12-01
How to Cite
1.
CHABROWSKI, Jan, SZULKIN, Andrzej and WILLEM, Michael. Schrödinger equation with multiparticle potential and critical nonlinearity. Topological Methods in Nonlinear Analysis. Online. 1 December 2009. Vol. 34, no. 2, pp. 201 - 211. [Accessed 23 April 2024].
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