Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting

M Del Pino, PL Felmer - Indiana University Mathematics Journal, 1999 - JSTOR
In this paper we consider a class of nonlinear singularly perturbed elliptic problems of the
form ε2Δu− u+ f (u)= 0 in Ω, for a superlinear, subcritical function f. Here Ω is a smooth
bounded domain, ε> 0 is a small parameter and we are interested in positive solutions to this
equation satisfying zero Dirichlet or Neumann boundary conditions on∂ Ω. In the study of
the asymptotic behavior of the solutions, when the parameter ε approaches zero, a key role
is played by a uniqueness-nondegeneracy assumption on the limiting equation. Our main …

Spike-layered Solutions of Singularly Perturbed Elliptic Problems in a Degenerate Setting

M Pino Manresa, P Felmer Aichele - 1999 - repositorio.uchile.cl
In this paper we consider a class of nonlinear singularly perturbed elliptic problems of the
form ε2 Δu-u+ f (u)= 0 in Ω, for a superlinear, subcritical function f. Here Ω a smooth bounded
domain, ε> 0 is a small parameter and we are interested in positive solutions to this equation
satisfying zero Dirichlet or Neumann boundary conditions on∂ Ω. In the study of the
asymptotic behavior of the solutions, when the parameter ε approaches zero, a key role is
played by a uniqueness-nondegeneracy assumption on the limiting equation. Our main …
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