A note on a system with radiation boundary conditions with non-symmetric linearisation

PABLO AMSTER; MARIEL PAULA KUNA

MONATSHEFETE FUR MATHEMATIK

SPRINGER WIEN

Lugar: Viena; Año: 2017

0026-9255

We prove the existence of multiple solutions for a second order ODE systemunder radiation boundary conditions. The proof is based on the degree computationof I − K , where K is an appropriate fixed point operator. Under a suitable asymptoticHartman-like assumption for the nonlinearity, we shall prove that the degree is 1 overlarge balls. Moreover, studying the interaction between the linearised system and thespectrum of the associated linear operator, we obtain a condition under which thedegree is −1 over small balls. We thus generalize a result obtained in a previous workfor the case in which the linearisation is symmetric.