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We consider the equation -ε 2 Δu = u p - u q in a bounded, smooth domain Ω ⊂ ℝ N with homogeneous Dirichlet boundary conditions when either. We prove the existence of multiple positive solutions in the case of small diffusion provided the domain Ω is not contractible. © 2012 by Pacific Journal of Mathematics

Deformation retracts to the fat diagonal and applications to the existence of peak solutions of nonlinear elliptic equations