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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. © 2017, Springer-Verlag GmbH Austria.

Registro:

Documento: Artículo
Título:A note on a system with radiation boundary conditions with non-symmetric linearisation
Autor:Amster, P.; Kuna, M.P.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
IMAS - CONICET, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Multiplicity; Radiation boundary conditions; Second order ODE systems; Topological degree
Año:2018
Volumen:186
Número:4
Página de inicio:565
Página de fin:577
DOI: http://dx.doi.org/10.1007/s00605-017-1098-y
Título revista:Monatshefte fur Mathematik
Título revista abreviado:Monatsh. Math.
ISSN:00269255
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00269255_v186_n4_p565_Amster

Referencias:

  • Amster, P., Multiple Solutions for an Elliptic System with Indefinite Robin Boundary Conditions, , To appear in Advances in Nonlinear Analysis
  • Amster, P., Kuna, M.P., Multiple solutions for a second order equation with radiation boundary conditions (2017) Electron. J. Qual. Theory Differ. Equ., 2017 (37), pp. 1-11
  • Amster, P., Kuna, M.P., On Exact Multiplicity for a Second Order Equation with Radiation Boundary Conditions, , Submitted
  • Amster, P., Kwong, M.K., Rogers, C., A Painlevé II model in two-ion electrodiffusion with radiation boundary conditions (2013) Nonlinear Anal. Real World Appl., 16, pp. 120-131
  • Bates, P., Solutions of nonlinear elliptic systems with meshed spectra (1980) Nonlinear Anal. Theory Methods Appl., 4 (6), pp. 1023-1030
  • Capietto, A., Dambrosio, W., Multiplicity results for systems of superlinear second order equations (2000) J. Math. Anal. Appl., 248, pp. 532-548
  • Capietto, A., Dambrosio, W., Papini, D., Detecting multiplicity for systems of second-order equations: an alternative approach (2005) Adv. Differ. Equ., 10 (5), pp. 553-578
  • Gritsans, A., Sadyrbaev, F., Yermachenko, I., Dirichlet boundary value problem for the second order asymptotically linear system (2016) Int. J. Differ. Equ., 2016, pp. 1-12
  • Hartman, P., On boundary value problems for systems of ordinary nonlinear second order differential equations (1960) Trans. Am. Math. Soc., 96, pp. 493-509
  • Lazer, A., Application of a lemma on bilinear forms to a problem in nonlinear oscillation (1972) Am. Math. Soc., 33, pp. 89-94
  • Smale, S., An infinite dimensional version of Sard’s theorem (1965) Am. J. Math., 87 (4), pp. 861-866
  • Yermachenko, I., Sadyrbaev, F., On a problem for a system of two second-order differential equations via the theory of vector fields (2015) Nonlinear Anal. Model. Control, 20 (2), pp. 175-189

Citas:

---------- APA ----------
Amster, P. & Kuna, M.P. (2018) . A note on a system with radiation boundary conditions with non-symmetric linearisation. Monatshefte fur Mathematik, 186(4), 565-577.
http://dx.doi.org/10.1007/s00605-017-1098-y
---------- CHICAGO ----------
Amster, P., Kuna, M.P. "A note on a system with radiation boundary conditions with non-symmetric linearisation" . Monatshefte fur Mathematik 186, no. 4 (2018) : 565-577.
http://dx.doi.org/10.1007/s00605-017-1098-y
---------- MLA ----------
Amster, P., Kuna, M.P. "A note on a system with radiation boundary conditions with non-symmetric linearisation" . Monatshefte fur Mathematik, vol. 186, no. 4, 2018, pp. 565-577.
http://dx.doi.org/10.1007/s00605-017-1098-y
---------- VANCOUVER ----------
Amster, P., Kuna, M.P. A note on a system with radiation boundary conditions with non-symmetric linearisation. Monatsh. Math. 2018;186(4):565-577.
http://dx.doi.org/10.1007/s00605-017-1098-y