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Solutions with spikes at the boundary for a 2D nonlinear Neumann problem with large exponent
Authors:Hernán Castro
Institution:Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
Abstract:We consider the elliptic equation −Δu+u=0 in a bounded, smooth domain Ω in R2, subject to the nonlinear Neumann boundary condition View the MathML source. 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 ξi∈∂Ω, in the sense that View the MathML source, as p→∞.
Keywords:Concentrating solutions  Large exponent  Green's function  Finite-dimensional reduction
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