Solutions with spikes at the boundary for a 2D nonlinear Neumann problem with large exponent

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Castro, Hernan^1,2 

[1] Univ Chile, Dept Ingn Matemat, Santiago, Chile

[2] Univ Chile, CMM, Santiago, Chile

关键词: Concentrating solutions;    Large exponent;    Green's function;    Finite-dimensional reduction;   

DOI  :  10.1016/j.jde.2009.02.001

来源: Elsevier

【 摘 要 】

We consider the elliptic equation -Delta u + u = 0 in a bounded, smooth domain Omega in R-2, subject to the nonlinear Neumann boundary condition partial derivative u/partial derivative v = u(p). Here p > 1 is a large parameter. We prove that given any integer m >= 1 there exist at least two families of solutions up developing exactly m peaks xi(1) is an element of partial derivative Omega in the sense that pu(p) -> 2e pi Sigma(m)(i=1) delta(xi i), as p -> infinity. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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