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Abstract:

TWe prove the existence of T−periodic solutions for the second order non-linear equation u0 1 − u02 0 = h(t)g(u), where the non-linear term g has two singularities and the weight function h changes sign. We find a relation between the degeneracy of the zeroes of the weight function and the order of one of the singularities of the non-linear term. The proof is based on the classical Leray-Schauder continuation theorem. Some applications to important mathematical models are presented. © 2018 American Institute of Mathematical Sciences. All rights reserved.

Registro:

Documento: Artículo
Título:Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity
Autor:Amster, P.; Zamora, M.
Filiación:Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Buenos Aires, 1428, Argentina
Departamento de Matemática Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Universidad de Oviedo, C/ Federico García Lorca, n18, Oviedo, Spain
Palabras clave:And phrases; Degree theory; Indefinite singularity; Leray-Schauder continuation theorem; Periodic solutions; Singular differential equations
Año:2018
Volumen:38
Número:10
Página de inicio:4819
Página de fin:4835
DOI: http://dx.doi.org/10.3934/dcds.2018211
Título revista:Discrete and Continuous Dynamical Systems- Series A
Título revista abreviado:Discrete Contin. Dyn. Syst. Ser A
ISSN:10780947
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v38_n10_p4819_Amster

Referencias:

  • Alexander, J.C., A primer on connectivity (1981) Proceeding of The Conference in Fixed Point Theory, 886, pp. 455-488. , Fadell, E.- Fournier, G. Editors, Springer-Verlag Lecture Notes in Mathematics
  • Bereanu, C., Gheorghe, D., Zamora, M., Periodic solutions for singular perturbations of the singular φ−Laplacian operator (2013) Commun. Contemp. Math., 15, p. 1250063. , 22
  • Bereanu, C., Gheorghe, D., Zamora, M., Non-resonant boundary value problems with singular φ-Laplacian operators (2013) Nonlinear Differential Equations and Applications, 20, pp. 1365-1377
  • Bereanu, C., Jebelean, P., Mawhin, J., Variational methods for nonlinear perturbations of singular φ−Laplacians (2011) Rend. Lincei Mat. Appl., 22, pp. 89-111
  • Bereanu, C., Mawhin, J., Existence and multiplicity results for some nonlinear problems with singular φ−Laplacian (2007) J. Differ. Equ., 243, pp. 536-557
  • Brezis, H., Mawhin, J., Periodic solutions of the forced relativistic pendulum (2010) Differ. Integral Equ., 23, pp. 801-810
  • Borisov, A.V., Mamaev, I.S., The restricted two body problem in constant curvature spaces (2006) Celestial Mech. Dynam. Astronom, 96, pp. 1-17
  • Borisov, A.V., Mamaev, I.S., Kilin, A.A., Two-body problem on a sphere. Reduction, stochasticity, periodic orbits (2004) Regul. Chaotic Dyn., 9, pp. 265-279
  • Boscaggin, A., Zanolin, F., Second-order ordinary differential equations with indefinite weight: The Neumann boundary value problem (2015) Ann. Mat. Pura Appl., 194, pp. 451-478
  • Bravo, J.L., Torres, P.J., Periodic solutions of a singular equation with indefinite weight (2010) Adv. Nonlinear Stud., 10, pp. 927-938
  • Capietto, A., Mawhin, J., Zanolin, F., Continuation theorems for periodic perturbations of autonomous systems (1992) Trans. Amer. Math. Soc., 329, pp. 41-72
  • Fitzpatrick, P., Martelli, M., Mawhin, J., Nussbaum, R., Topological methods for ordinary differential equations (1991) Lecture Notes in Mathematics, 1537, pp. 1-209. , Springer-Verlag
  • Fonda, A., Manásevich, R., Zanolin, F., Subharmonic solutions for some second-order differential equations with singularities (1993) SIAM J. Math. Anal., 24, pp. 1294-1311
  • Hakl, R., Zamora, M., On the open problems connected to the results of Lazer and Solimini (2014) Proc. Roy. Soc. Edinb., Sect. A. Math., 144, pp. 109-118
  • Hakl, R., Zamora, M., Periodic solutions of an indefinite singular equation arising from the Kepler problem on the sphere (2018) Canadian J. Math., 70, pp. 173-190
  • Hutten, E.H., Relativistic (non-linear) oscillator (1965) Nature, 203, p. 892
  • Lazer, A.C., Solimini, S., On periodic solutions of nonlinear differential equations with singularities (1987) Proc. Amer. Math. Soc., 99, pp. 109-114
  • Mac-Coll, L.A., Theory of the relativistic oscillator (1957) Am. J. Phys., 25, pp. 535-538
  • Torres, P.J., Nondegeneracy of the periodically forced Liénard differential equations with φ−Laplacian (2011) Commun. Contemp. Math., 13, pp. 283-293
  • Ureña, A.J., Periodic solutions of singular equations (2016) Topological Methods in Nonlinear Analysis, 47, pp. 55-72
  • Whyburn, G.T., (1958) Topological Analysis, , Princeton Univ. Press
  • Zamora, M., New periodic and quasi-periodic motions of a relativistic particle under a planar central force field with applications to scalar boundary periodic problems (2013) J. Qualitative Theory of Differential Equations, 31, pp. 1-16

Citas:

---------- APA ----------
Amster, P. & Zamora, M. (2018) . Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity. Discrete and Continuous Dynamical Systems- Series A, 38(10), 4819-4835.
http://dx.doi.org/10.3934/dcds.2018211
---------- CHICAGO ----------
Amster, P., Zamora, M. "Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity" . Discrete and Continuous Dynamical Systems- Series A 38, no. 10 (2018) : 4819-4835.
http://dx.doi.org/10.3934/dcds.2018211
---------- MLA ----------
Amster, P., Zamora, M. "Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity" . Discrete and Continuous Dynamical Systems- Series A, vol. 38, no. 10, 2018, pp. 4819-4835.
http://dx.doi.org/10.3934/dcds.2018211
---------- VANCOUVER ----------
Amster, P., Zamora, M. Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity. Discrete Contin. Dyn. Syst. Ser A. 2018;38(10):4819-4835.
http://dx.doi.org/10.3934/dcds.2018211