Periodic solutions of singular equations

Antonio Ureña

DOI: http://dx.doi.org/10.12775/TMNA.2015.087

Abstract


We study second-order ordinary differential equations of Newtonian type. The forcing terms under consideration are the product of a nonlinearity which is singular at the origin with an indefinite weight. Under some additional assumptions we show the existence of periodic solutions.

Keywords


Periodic solutions; singular equations; indefinite weight

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References


R. Agarwal and D. O'Regan, A Survey of recent results for initial and boundary value problems singular in the dependent variable, Handbook of Differential Equations, 1-68, Elsevier/North-Holland, Amsterdam, 2004.

L.E. Bobisud, D. O'Regan and W.D. Royalty, Solvability of some nonlinear boundary value problems, Nonlinear Anal. 12 (1988), no. 9, 855-869.

A. Boscaggin and F. Zanolin, Second order ordinary differential equations with indefinite weight: the Neumann boundary value problem, Preprint, 2013.

J.L. Bravo and P.J. Torres, Periodic solutions of a singular equation with indefinite weight, Adv. Nonlinear Stud. 10 (2010), no. 4, 927-938.

E.N. Dancer, On the use of asymptotics in nonlinear boundary value problems, Ann. Mat. Pura Appl. (4) 131 (1982), 167-185.

C. De Coster and P. Habets, Two-Point Boundary Value Problems: Lower and Upper Solutions, Mathematics in Science and Engineering, 205, Elsevier B.V., Amsterdam, 2006.

J.A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second-order ordinary differential equations J. Differential Equations 79 (1989), no. 1, 62-78.

M. Gaudenzi, P. Habets and F. Zanolin, Positive solutions of singular boundary value problems with indefinite weight, Bull. Belg. Math. Soc. 9 (2002), 607-619.

W.B. Gordon, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc. 204 (1975), 113-135.

Z. Guo, Solvability of some singular nonlinear boundary value problems and existence of positive radial solutions of some nonlinear elliptic problems, Nonlinear Anal. 16 (1991), no. 9, 781-790.

P. Habets and F. Zanolin, Upper and lower solutions for a generalized Emden-Fowler equation, J. Math. Anal. Appl. 181 (1994), no. 3, 684-700.

J. Janus and J. Myjak, A generalized Emden-Fowler equation with a negative exponent, Nonlinear Anal. 23 (1994), no. 8, 953-970.

C.D. Luning and W.L. Perry, Positive solutions of negative exponent generalized Emden-Fowler boundary value problems, SIAM J. Math. Anal. 12 (1981), no. 6, 874-879.

A. Nachman and A. Callegari, A nonlinear singular boundary value problem in the theory of pseudoplastic uids, SIAM J. Appl. Math. 38 (1980), no. 2, 275-281.

A.J. Ure~na, Some counterexamples for singular equations with indefinite weight, in preparation.

S.D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), no. 6, 897-904.


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