65 citations · 104 across the 2 of their papers we have counts for
6 papers
Dual ground state solutions for the critical nonlinear Helmholtz equation
Gilles Evéquoz, Tolga Yesil
Using a dual variational approach we obtain nontrivial real-valued solutions of the critical nonlinear Helmholtz equation $$ - Δu - k^{2}u = Q(x)|u|^{2^{\ast} - 2}u, \quad u \in W^…
Multiple standing waves for the nonlinear Helmholtz equation concentrating in the high frequency limit
Gilles Evéquoz
This paper studies for large frequency number the existence and multiplicity of solutions of the semilinear problem $$ -Δu -k^2 u=Q(x)|u|^{p-2}u\quad\text{ in }\mathbb{R}^N,…
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…
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 , …
Dual variational methods and nonvanishing for the nonlinear Helmholtz equation
Gilles Evequoz, Tobias Weth
We set up a dual variational framework to detect real standing wave solutions of the nonlinear Helmholtz equation …
Real solutions to the nonlinear Helmholtz equation with local nonlinearity
Gilles Evequoz, Tobias Weth
In this paper, we study real solutions of the nonlinear Helmholtz equation satisfying the asymptotic conditions $$ u(x)=O(|x|^{\frac{1-…