Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in ℝn
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In 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.
CitationVisetti, D. (2005). Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in Rn. Electronic Journal of Differential Equations, 2005(05), pp. 1-20.
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