Geodesic
Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in $\Bbb R^n$
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we study the nonlinear eigenvalue field equation $$ -\Delta u+V(|x|)u+\varepsilon(-\Delta_p u+W'(u))=\mu u $$ where $u$ is a function from $\mathbb{R}^n$ to $\mathbb{R}^{n+1}$ with $n\geq 3, \varepsilon$ is a positive parameter and $O(n)$: For any $q\in\mathbb{Z}$ we prove the existence of finitely many pairs $(u,\mu)$ solutions for $\varepsilon$ sufficiently small, where $u$ is symmetric and has topological charge $q$. The multiplicity of our solutions can be as large as desired, provided that the singular point of $W$ and $\varepsilon$ are chosen accordingly.
Classification : 35Q55, 45C05
Keywords: nonlinear Schrödinger equations, nonlinear eigenvalue problems 
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     author = {Visetti, Daniela},
     title = {Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in $\Bbb R^n$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a186/}
}
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Visetti, Daniela. Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in $\Bbb R^n$. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a186/