Multiple boundary peak solutions for some singularly perturbed Neumann problems

By Changfeng Gui, Jun-cheng Wei, Matthias Winter. 2000

225 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/14cd0e2f6921b99a4a658713b09cf954054ed65b

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Semilinear Neumann boundary value problems on a rectangle (2002, background): “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.”
Boundary concentration phenomena for a singularly perturbed elliptic problem (2002, background): “In [20]–[22] the authors prove existence of solutions with an increasing number of peaks.”
Multiple clustered layer solutions for semilinear Neumann problems on a ball (2005, background): “For example, if the bound ary mean curvature has a local minimum point P0, then it is shown [15] that given arbitrary positive integer K , there exists a boundary spike solution with K spikes concentrating near P0.”
Singularly Perturbed Elliptic Equations with Symmetry: Existence of Solutions Concentrating on Spheres, Part I (2003, unknown): “[10, 11, 14, 15, 17 , 19, 24 ]a nd references therein.”
Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory (2000, background): “In [7] and [ 13 ] it was proved that for any fixed positive integer K there exists a boundary K−peak solution at a local minimum point of H(x), whose local maximum points collapse at the same point of the boundary.”
Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity Part I: N=3 (2004, background): “Higher energy solutions exist which blow up at one or several points, located on the boundary [8][13][22][33][19], in the interior of the domain [5][7][11][12][16][21][38][40], or some of them on the boundary and others in the interior [18].”
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].”
Chapter 6 Existence and stability of spikes for the Gierer-Meinhardt system (2008, methodology): “THEOREM 2.2. (See [9, 29 ].) Let Γ be a subset of ∂Ω, where it holds”
The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds (2009, background): “Later, in [5,25] it has been proved that for any stable critical point of H one can construct single boundary spike layer, while in [10,20,27] the authors construct multiple boundary spike layer solutions at multiple stable critical points of H. Finally, in [ 12 ] the authors proved that for any int”
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.”