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On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems. (English) Zbl 0947.35073

Summary: Multi-peaked solutions to a singularly perturbed elliptic equation on a bounded domain \(\Omega\) are constructed, provided the distance function \(d(x,\partial\Omega)\) has more than one strict local maximum.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B25 Singular perturbations in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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