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Existence and asymptotic behavior of standing waves of the nonlinear Helmholtz equation in the plane by Gilles Evéquoz is a Mathematics article available to read on EtoBox.
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## Abstract In this paper we study the semilinear elliptic problem - Δ u - k 2 u = Q | u | p - 2 u in R 2 , -\Delta u-k^{2}u=Q|u|^{p-2}u\quad\text{in }\mathbb{R}^{2}, where k > 0 {k>0} , p ≥ 6 {p\geq 6} and __Q__ is a bounded function. We prove the existence of real-valued W 2 , p {W^{2,p}} -solutions, both for decaying and for periodic coefficient __Q__. In addition, a nonlinear far-field relation is derived for these solutions.
Who reads Existence and asymptotic behavior of standing waves of the nonlinear Helmholtz equation in the plane?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Gilles Evéquoz
- Publisher
- Walter de Gruyter GmbH
- Published
- 2017
- Language
- EN
- Field
- Mathematics (Physical Sciences)