Abstract
In this article we shall review some recent progress in the study of the Neumann problem for a semilinear elliptic equation. Let Ω be a bounded domain in R N, N ≥ 2, with smooth boundary ∂Ω and let v denote the unit outer normal to ∂Ω. We consider the Neumann problem in which is the Laplace operator, d is a positive constant and throughout the article we assume that unless it is explicitly stated otherwise. (Most of the results below do generalize to a certain class of functions f including t p, and the reader is referred to the original papers cited.)
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© 1992 Springer Science+Business Media New York
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Ni, WM., Takagi, I. (1992). On the Existence and Shape of Solutions to a Semilinear Neumann Problem. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_29
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DOI: https://doi.org/10.1007/978-1-4612-0393-3_29
Publisher Name: Birkhäuser, Boston, MA
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