Visetti, Daniela2021-05-182021-05-182005-01-02Visetti, D. (2005). Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in Rn. <i>Electronic Journal of Differential Equations, 2005</i>(05), pp. 1-20.1072-6691https://hdl.handle.net/10877/13576In this paper, we study the nonlinear eigenvalue field equation -Δu + V(|x|)u + ε(-Δpu + W'(u)) = μu where u is a function from ℝn to ℝn+1 with n ≥ 3, ε is a positive parameter and p > n. We fine a multiplicity of solutions, symmetric with respect to an action of the orthogonal group O(n): For any q ∈ ℤ we prove the existence of finitely many pairs (u, μ) solutions for ε 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 ε are chosen accordingly.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear Schrödinger equationsNonlinear eigenvalue problemsArticle