Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in ℝn
Date
2005-01-02
Authors
Visetti, Daniela
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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.
Description
Keywords
Nonlinear Schrödinger equations, Nonlinear eigenvalue problems
Citation
Visetti, 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.
Rights
Attribution 4.0 International