Singularly perturbed nonlinear Dirichlet problems involving critical growth

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We consider the following singularly perturbed nonlinear elliptic problem: -epsilon(2)Delta u + u = f (u), u > 0 on Omega, u = 0 on partial derivative Omega, where Omega is a bounded domain in R-N (N = 3) with a boundary partial derivative Omega is an element of C-2 and the nonlinearity f is of critical growth. In this paper, we construct a solution u(epsilon) of the above problem which exhibits one spike near a maximum point of the distance function from the boundary partial derivative Omega under a critical growth condition on f. Our result complements the study made in [9] in the sense that, in that paper, only the subcritical growth was considered.
Publisher
SPRINGER
Issue Date
2013-05
Language
English
Article Type
Article
Citation

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v.47, no.1-2, pp.65 - 85

ISSN
0944-2669
DOI
10.1007/s00526-012-0511-6
URI
http://hdl.handle.net/10203/209385
Appears in Collection
MA-Journal Papers(저널논문)
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