On Singular Perturbation Problems with Robin Boundary Condition
نویسندگان
چکیده
We consider the following singularly perturbed elliptic problem 2 u ? u + f(u) = 0; u > 0 in ; @u @ + u = 0 on @; where f satisses some growth conditions, 0 +1, and R N (N > 1) is a smooth and bounded domain. The cases = 0 (Neumann problem) and = +1 (Dirichlet problem) have been studied by many authors in recent years. We show that, there exists a generic constant > 1 such that, as ! 0, the least energy solution has a spike near the boundary if , and has an interior spike near the innermost part of the domain if >. Central to our study is the corresponding problem on the half space.
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