Search

We consider the following singularly perturbed nonlinear elliptic problem: where Ω is a bounded domain in $${\mathbb{R}^N (N \ge 3)}$$ with a boundary $${\partial \Omega \in C^2}$$ and the nonlinearity f is of critical growth. In this paper, we construct a solution $${u_\varepsilon}$$ of the above problem which exhibits one spike near a maximum point of the distance function from the boundary ∂Ω under a critical growth condition on f. Our result complements the study made in [] in the sense that, in that paper, only the subcritical growth was considered. [ABSTRACT FROM AUTHOR]

Abstract: We consider the following singularly perturbed nonlinear elliptic problemwhere the nonlinearity f is of subcritical growth and is a bounded domain in . Under certain conditions of there exists a mountain pass solution for above problem and the solution exhibits a spike layer as . To see the location of the spike layer for small some additional assumptions, certain nondegeneracy for a limiting problem or monotonicity of have been assumed. In this paper, we characterize the location of the spike layer without such additional assumptions for . [Copyright &y& Elsevier]