Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres

DOI10.1016/J.JDE.2011.10.004zbMath1232.35057arXiv1009.2600OpenAlexW1970872776MaRDI QIDQ652462

Jonathan Di Cosmo, Denis Bonheure, Jean Van Schaftingen

Publication date: 14 December 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2600

zbMATH Keywords

semilinear elliptic problemradial solutionsingular potentialsemiclassical statesvanishing potentialconcentration on submanifoldsstationary nonlinear Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

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