Geodesic
Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in \(\mathbb R^n\)
Electronic journal of differential equations, Tome 2005 (2005)
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 
@article{EJDE_2005__2005__a286,
     author = {Visetti,  Daniela},
     title = {Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in \(\mathbb {R^n\)}},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1070.35096},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a286/}
}
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%J Electronic journal of differential equations
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Visetti,  Daniela. Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in \(\mathbb R^n\). Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a286/