On the periodic and asymptotically periodic nonlinear Helmholtz equation. (March 2017) - Evéquoz, Gilles
Abstract: In the first part of this paper, the existence of infinitely many L p -standing wave solutions for the nonlinear Helmholtz equation − Δ u − λ u = Q ( x ) ∣ u ∣ p − 2 u in R N is proven for N ≥ 2 and λ > 0, under the assumption that Q be a nonnegative, periodic and bounded function and the exponent p lies in the Helmholtz subcritical range. In a second part, the existence of a nontrivial solution is shown in the case where the coefficient Q is only asymptotically periodic.