Asymptotic behavior of least energy solutions for a singularly perturbed problem with nonlinear boundary condition
Tóm tắt
We consider the problem of finding a positive harmonic function
$$u_\varepsilon $$
in a bounded domain
$$\Omega \subset \mathbb R ^N (N\ge 3)$$
satisfying a nonlinear boundary condition of the form
$$\varepsilon \partial _{\nu } u +u =|u|^{p-2}u,\,x\in \partial \Omega $$
, where
$$\varepsilon $$
is a positive parameter and
$$2
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