A note on a system with radiation boundary conditions with non-symmetric linearisation
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 pro...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00269255_v186_n4_p565_Amster |
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| Sumario: | 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. © 2017, Springer-Verlag GmbH Austria. |
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