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Normalized solutions of nonlinear Schr\"odinger equations

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arxiv 1209.0950 v1 pith:URAY3NMK submitted 2012-09-05 math.AP

Thomas Bartsch , Sébastien de Valeriola This is my paper · ORCID
classification math.AP
keywords lambdasolutionsassociatedbelowboundedcaseconsiderdeal
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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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  1. Multiplicity and asymptotic behavior of normalized solutions to p-Kirchhoff equations

    math.AP 2024-11 conditional novelty 6.0 of 10

    For the p-Kirchhoff equation with prescribed L^p mass in R^3, the paper establishes the existence-nonexistence trichotomy, radial ground states and infinitely many high-energy solutions in the supercritical range, and...

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