Volume 14, Issue 4
Remarks on the Shape of Least-energy Solutions to a Semilinear Dirichlet Problem
DOI:

J. Part. Diff. Eq., 14 (2001), pp. 365-383.

Published online: 2001-11

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• Abstract

Structure of least-energy solutions to singularly perturbed semilinear Dirichlet problem ε²Δu - u^α + g(u) = 0 in Ω,u = 0 on ∂Ω, Ω ⊂ ⋅R^N a bounded smooth domain, is precisely studied as ε → 0^+, for 0 < α < 1 and a superlinear, subcritical nonlinearity g(u). It is shown that there are many least-energy solutions for the problem and they are spike-layer solutions. Moreover, the measure of each spike-layer is estimated as ε → 0^+ .

• Keywords

Least-energy solutions spike-layer solutions singularly perturbed semilinear Dirichlet problem nontrivial nonnegative solutions