Abstract
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 \(I-K\), 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 \(-1\) over small balls. We thus generalize a result obtained in a previous work for the case in which the linearisation is symmetric.
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Acknowledgements
The authors thank the referees for the careful reading of the manuscript and insightful comments. This work was partially supported by projects UBACyT 20020120100029BA and CONICET PIP 11220130100006CO.
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Communicated by A. Jüngel.
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Amster, P., Kuna, M.P. A note on a system with radiation boundary conditions with non-symmetric linearisation. Monatsh Math 186, 565–577 (2018). https://doi.org/10.1007/s00605-017-1098-y
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DOI: https://doi.org/10.1007/s00605-017-1098-y