10 citations · 24 across the 5 of their papers we have counts for
6 papers
Dual variational methods for a nonlinear Helmholtz equation with sign-changing nonlinearity
Rainer Mandel, Dominic Scheider, Tolga Yesil
We prove new existence results for a Nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$ - Δu - k^{2}u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}(\mathbb{R}^{N})…
Variational methods for breather solutions of Nonlinear Wave Equations
Rainer Mandel, Dominic Scheider
We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These solutions are obtained from critical points of a dual funct…
Breather Solutions of the Cubic Klein-Gordon Equation
Dominic Scheider
We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein-Gordon equation \begin{align} \partial_t^2 U - ΔU + m^2 U = Γ(x) U^3 \quad \text{on } \math…
An annulus multiplier and applications to the Limiting absorption principle for Helmholtz equations with a step potential
Rainer Mandel, Dominic Scheider
We consider the Helmholtz equation on where the potential is constant on each of the half-spaces $\mathbb{R}^…
Bifurcations of nontrivial solutions of a cubic Helmholtz system
Rainer Mandel, Dominic Scheider
This paper presents local and global bifurcation results for radially symmetric solutions of the cubic Helmholtz system \begin{equation*} \begin{cases} -Δu - μu = \left( u^2 + b \:…
Dual Variational Methods for a nonlinear Helmholtz system
Rainer Mandel, Dominic Scheider
This paper considers a pair of coupled nonlinear Helmholtz equations \begin{align*} -Δu - μu = a(x) \left( |u|^\frac{p}{2} + b(x) |v|^\frac{p}{2} \right)|u|^{\frac{p}{2} - 2}u, \en…