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Concentration of solutions of equations of nonlinear Schrödinger type with vector potential: infinite-bump solutions and non-degeneracy

Part of: Elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  22 March 2016

Robert Magnus
Robert Magnus*
Affiliation:
The University Science Institute, University of Iceland, Dunhaga 3, 107-Reykjavik, Iceland (robmag@hi.is)
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Extract

The equation –ε2Δu + F(V(x), u) = 0 is studied over all of ℝn, and solutions are constructed that concentrate at an infinite set as ε → 0. The function V (x) is vector valued. This advances previous studies in which V (x) was scalar valued.

Keywords

nonlinear Shrödinger equationconcentrationinfinite-bump solution

MSC classification

Secondary: 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian 35B25: Singular perturbations

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 3 , June 2016 , pp. 625 - 646
Copyright
Copyright © Royal Society of Edinburgh 2016 

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