## Normalized solutions of nonlinear Schrödinger equations.(English)Zbl 1260.35098

Summary: We consider the problem \left\{\begin{aligned} & -\Delta u - g(u) = \lambda u, \\ & u \in H^1(\mathbb{R}^N), \int_{\mathbb{R}^N} u^2 = 1, \lambda \in \mathbb{R},\end{aligned}\right. in dimension $$N \geq 2$$. 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.

### MSC:

 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) 35J60 Nonlinear elliptic equations 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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### References:

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