Lin, Chang-Shou; Wei, Juncheng Uniqueness of multiple-spike solutions viat the method of moving planes. (English) Zbl 1141.35008 Pure Appl. Math. Q. 3, No. 3, 689-735 (2007). Summary: We study the uniqueness of multiple-spike solutions for some singularly perturbed Neumann problems in a ball. We completely classify all two-peaked solutions and, except in some degenerate situations, also all three-peaked solutions. Our main idea is using the method of moving planes to show that in the case of two peaks both of them must be located on a line containing the origin and for three peaks all of them must lie in a two-dimensional hyperplane containing the origin. Then we compute the degree of these solutions (restricted to a certain symmetry class) and show their uniqueness. Cited in 1 Document MSC: 35B25 Singular perturbations in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35B45 A priori estimates in context of PDEs 35J40 Boundary value problems for higher-order elliptic equations 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:Neumann problems in a ball; symmetry class PDFBibTeX XMLCite \textit{C.-S. Lin} and \textit{J. Wei}, Pure Appl. Math. Q. 3, No. 3, 689--735 (2007; Zbl 1141.35008) Full Text: DOI