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Solutions to a nonlinear Maxwell equation with two competing nonlinearities in R3

Bieganowski Bartosz

Bulletin of the Polish Academy of Sciences. Mathematics

2021

Vol. 69, no. 1

37--60

We are interested in the nonlinear, time-harmonic Maxwell equation ∇(∇E)+V(x)E=h(x,E) in R3 with sign-changing nonlinear term h, i.e. we assume that h is of the form h(x,αw)=f(x,α)w−g(x,α)w for w∈R3, |w|=1 and α∈R. In particular, we can consider the nonlinearity consisting of two competing powers, h(x,E)=|E|p−2E−|E|q−2E with 2