Normalized solutions of nonlinear Schr\"odinger equations

Thomas Bartsch; Sébastien de Valeriola

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arXiv · 1209.0950

Normalized solutions of nonlinear Schr\"odinger equations

Thomas Bartsch·Sébastien de Valeriola

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Abstract

We consider the problem -\Delta u - g(u) = \lambda u, u \in H^1(\R^N), \int_{\R^N} u^2 = 1, \lambda\in\R, in dimension $N\ge2$. Here $g$ is a superlinear, subcritical, possibly nonhomogeneous, odd nonlinearity. We deal with the case where the associated functional is not bounded below on the $L^2$-unit sphere, and we show the existence of infinitely many solutions.

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Thomas Bartsch, Sébastien de Valeriola. 2012-09-05. Normalized solutions of nonlinear Schr\"odinger equations. https://arxiv.org/abs/1209.0950

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