A note on a system with radiation boundary conditions with non-symmetric linearisation
Monatshefte fur Mathematik, 2018, 186(4): 565-577.
We prove the existence of multiple solutions for a second order ODE system under radiation boundary conditions. The proof is based on the degree computation of , where K is an appropriate fixed point operator. Under a suitable asymptotic Hartman-like assumption for the nonlinearity, we shall prove that the degree is 1 over large balls. Moreover, studying the interaction between the linearised system and the spectrum of the associated linear operator, we obtain a condition under which the degree is over small balls. We thus generalize a result obtained in a previous work for the case in which the linearisation is symmetric.
Second order ODE systems; Radiation boundary conditions; Multiplicity; Topological degree