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