On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems

By Changfeng Gui, Jun-cheng Wei. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2000

165 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1aaf61565c44c5479972d07234a5968eb7c0cc89

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In Applied Mathematics

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Citations in the corpus

Semilinear Neumann boundary value problems on a rectangle (2002, unknown): “In recent years, the spike layer solutions have been the subjects of numerous studies; see, for example, [BDS], [BS], [BFi], [BFu], [DY1], [DY2], [G], [GW1], [ GW2 ], [GWW], [Kow], [L], [LNT], [NT2], [NT3], [W], [WW1], [WW2] and references therein.”
Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3 (2005, unknown): “A combination of the LiapunovSchmidt reduction method and the variational principle was used in [3, 10, 11, 15] and [16].”
Singularly Perturbed Elliptic Equations with Symmetry: Existence of Solutions Concentrating on Spheres, Part I (2003, methodology): “Remark 1.13. For the construction of the approximate solutions in ZN (or in ZD for the Dirichlet case, see Sections 3, 4) we follow mainly the approach of [ 16 ].”
Boundary concentration phenomena for a singularly perturbed elliptic problem (2002, background): “There are other types of solutions of (Pε) with interior and/or boundary peaks, possibly multiple, which are constructed by using gluing techniques or topological methods; see [9, 8, 20, 21, 22, 39].”
Bubbling solutions for an anisotropic Emden–Fowler equation (2006, unknown): “other papers. See for instance [4], [11], [9], [15], [ 16 ], [17], [13], [25] and references therein.”
Chapter 6 Existence and stability of spikes for the Gierer-Meinhardt system (2008, background): “THEOREM 2.4. (See [ 28 ].) For any two fixed positive integers k, l, there exists � k,l such that for �< � k,l, problem (2.4) has a solution u� with k interior local maximum points and l boundary maximum points.”
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains (2005, background): “There exists solutions with an arbitrary large number of peaks (of multibump type) at the boundary and in the interior of @›, see [8], [12], [17], [18], [20], [24], [40], [42], and in particular [ 19 ].”
Multiple clustered layer solutions for semilinear Neumann problems on a ball (2005, result): “We m one result which is related to our work here: in [14], it was proved that for any two integers k 0, l 0, k + l > 0, problem (1.”