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dc.contributor.authorVisetti, Daniela ( )
dc.identifier.citationVisetti, D. (2005). Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in Rn. Electronic Journal of Differential Equations, 2005(05), pp. 1-20.en_US

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.

dc.format.extent20 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectNonlinear Schrödinger equationsen_US
dc.subjectNonlinear eigenvalue problemsen_US
dc.titleMultiplicity of symmetric solutions for a nonlinear eigenvalue problem in ℝnen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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