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math.AP2016
Multiple standing waves for the nonlinear Helmholtz equation concentrating in the high frequency limit
Gilles Evéquoz
This paper studies for large frequency number the existence and multiplicity of solutions of the semilinear problem $$ -Δu -k^2 u=Q(x)|u|^{p-2}u\quad\text{ in }\mathbb{R}^N,…
math.AP2016
Existence and asymptotic behavior of standing waves of the nonlinear Helmholtz equation in the plane
Gilles Evéquoz
In this paper we study the semilinear elliptic problem where , and is a bounded function. We prove the e…
math.AP2016
Branch continuation inside the essential spectrum for the nonlinear Schrödinger equation
Gilles Evéquoz, Tobias Weth
We consider the nonlinear stationary Schrödinger equation \begin{equation*} -Δu -λu= Q(x)|u|^{p-2}u, \qquad \text{in }\mathbb{R}^N \end{equation*} in the case where , …