Remarks on the Shape of Least-energy Solutions to a Semilinear Dirichlet Problem

Remarks on the Shape of Least-energy Solutions to a Semilinear Dirichlet Problem

Year:    2001

Journal of Partial Differential Equations, Vol. 14 (2001), Iss. 4 : pp. 365–383

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^+ .

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2001-JPDE-5490

Journal of Partial Differential Equations, Vol. 14 (2001), Iss. 4 : pp. 365–383

Published online:    2001-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Least-energy solutions