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Abstract:

Motivated by the classical Coulomb central motion model, we study the existence of Tperiodic solutions for the nonlinear second order system of singular ordinary differential equations u'' + g(u) = p(t). Using topological degree methods, we prove that when the nonlinearity g : RN\\{0} ← RN is continuous, repulsive at the origin and bounded at infinity, if an appropriate Nirenberg type condition holds then either the problem has a classical solution, or else there exists a family of solutions of perturbed problems that converge uniformly and weakly in H1 to some limit function u. Furthermore, under appropriate conditions we prove that u is a classical solution.

Registro:

Documento: Artículo
Título:Periodic solutions of systems with singularities of repulsive type
Autor:Amster, P.; Maurette, M.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
Palabras clave:Periodic solutions; Repulsive singularities; Topological degree
Año:2011
Volumen:11
Número:1
Página de inicio:201
Página de fin:220
DOI: http://dx.doi.org/10.1515/ans-2011-0110
Título revista:Advanced Nonlinear Studies
Título revista abreviado:Adv. Nonlinear Stud.
ISSN:15361365
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v11_n1_p201_Amster

Referencias:

  • Ambrosetti, V., Coti Zelati, A., (1993) Periodic Solutions of Singular Lagrangian Systems, , Birkhäuser, Boston
  • Amster, P., De Napoli, P., Landesman-Lazer type conditions for a system of p-Laplacian like operators (2007) Journal of Mathematical Analysis and Applications, 326 (2), pp. 1236-1243. , DOI 10.1016/j.jmaa.2006.04.001, PII S0022247X06003477
  • Bahri, A., Rabinowitz, P., A minimax method for a class of hamiltonian systems with singular potentials (1989) J. Funct. Anal., 82 (2), pp. 412-428
  • Chu, J., Torres, P., Zhang, M., Periodic solutions of second order non-autonomous singular dynamical systems (2007) J. Differential Equations, 239 (12), pp. 196-212
  • Coti Zelati, V., Dynamical systems with effective-like potentials (1988) Nonlinear Anal., 12 (2), pp. 209-222
  • Fonda, A., Toader, R., Periodic orbits of radially symmetric Keplerian-like systems: A topological degree approach (2008) J. Differential Equations, 244 (12), pp. 3235-3264
  • Gordon, W., Conservative dynamical systems involving strong forces (1975) Trans. Amer. Math. Soc., 204, pp. 113-135
  • Hartman, P., On boundary value problems for systems of ordinary nonlinear second order differential equations (1960) Trans. Amer. Math. Soc., 96, pp. 493-509
  • Landesman, E.M., Lazer, A.C., Nonlinear perturbations of linear elliptic boundary value problems at resonance (1969) J. Math. Mech., 19, pp. 609-623
  • Lazer, A.C., On Schauder's fixed point theorem and forced second-order nonlinear oscillations (1968) J. Math. Anal. Appl., 21, pp. 421-425
  • Lazer, A.C., Solimini, S., On periodic solutions of nonlinear differential equations with singularities (1987) Proc. Amer. Math. Soc., 99 (1), pp. 109-114
  • Mawhin, J., Topological degree methods in nonlinear boundary value problems (1977) CBMS Regional Conference Series in Mathematics, 40. , American Mathematical Society, Providence, R.I. Expository lectures from the CBMS Regional Conference held at Harvey Mudd College, Claremont, Calif., June 9-15
  • Nirenberg, L., Generalized degree and nonlinear problems (1971) Contributions to Nonlinear Functional Analysis, pp. 1-9. , Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971. Academic Press, New York
  • Ortega, R., Ward Jr., J.R., A semilinear elliptic system with vanishing nonlinearities (2002) Discrete Contin. Dyn. Syst., (SUPPL.), pp. 688-693. , Dynamical Systems and Differential Equations (Wilmington, NC)
  • Ruiz, D., Ward, J.R., Some notes on periodic systems with linear part at resonance (2004) Discrete and Continuous Dynamical Systems, 11 (2-3), pp. 337-350
  • Solimini, S., On forced dynamical systems with a singularity of repulsive type (1990) Nonlinear Anal., 14 (6), pp. 489-500
  • Torres, P.J., Non-collision periodic solutions of forced dynamical systems with weak singularities (2004) Discrete and Continuous Dynamical Systems, 11 (2-3), pp. 693-698
  • Zhang, M., Periodic solutions of damped differential systems with repulsive singular forces (1999) Proc. Amer. Math. Soc., 127 (2), pp. 401-407

Citas:

---------- APA ----------
Amster, P. & Maurette, M. (2011) . Periodic solutions of systems with singularities of repulsive type. Advanced Nonlinear Studies, 11(1), 201-220.
http://dx.doi.org/10.1515/ans-2011-0110
---------- CHICAGO ----------
Amster, P., Maurette, M. "Periodic solutions of systems with singularities of repulsive type" . Advanced Nonlinear Studies 11, no. 1 (2011) : 201-220.
http://dx.doi.org/10.1515/ans-2011-0110
---------- MLA ----------
Amster, P., Maurette, M. "Periodic solutions of systems with singularities of repulsive type" . Advanced Nonlinear Studies, vol. 11, no. 1, 2011, pp. 201-220.
http://dx.doi.org/10.1515/ans-2011-0110
---------- VANCOUVER ----------
Amster, P., Maurette, M. Periodic solutions of systems with singularities of repulsive type. Adv. Nonlinear Stud. 2011;11(1):201-220.
http://dx.doi.org/10.1515/ans-2011-0110