Layer solutions in a half-space for boundary reactions.(English)Zbl 1102.35034

The article is concerned with the nonlinear problem $$\Delta u=0$$ in $$\mathbb R^n_+$$, $$\partial u/\partial \nu = f(u)$$ on $$\partial \mathbb R^n_+$$. The existence, uniqueness, symmetry, variational properties and asymptotic behavior of layer solutions of this problem is studied. For $$n=2$$ the characterization of $$f$$, for which there exists a layer solution, is given.

MSC:

 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:

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