References
- De Coster , C. and Habets , P. 1996 . “ Lower and upper solutions in the theory of ODE boundary value problems:Classical and recent results. ” . In In: Nonlinear Analysis and Boundary Valuefor Ordinary Differential Equations. , Vol. 371 , 1 – 78 . Wien : Springer-Verlag . CISM Courses and Lectures.
- Del Pino , M. and Manásevich , R. 1992 . T-periodic Solutions for some second order differential equations with singulartues . Proc.Royal.Soc. , 120A, : 231 – 244 .
- Fonda , A. , Manásevich , R. and Zanolin , F. 1993 . Subharmonic for some second-rder diferential equations with singularities . SIAM J.Math.Anal., , 24 : 1294 – 1311 .
- Gaines , R.E. and Mawhin , J. 1997 . “ Coincidence Degree and Nonliner Differential Equations ” . In Lecture Notes in Math. , 568 Berlin : Springer-Verlag .
- Habets , P. and Sanchez , L. 1990 . Periodic solutions of some Liénard equations with singularities . Proc.Amer.Math.Soc., , 109 : 1035 – 1044 .
- Kiguradze I. Some Singular Boundary Value Problems for Ordinary Differential Equations ITU Tbilisi 1975 (in Russian)
- Knobloch , H.W. 1963 . Eine neue Methode Zur Approximation periodischer Lösungen nicht-linearer Differential Gleichungen Zweiter Ordnug. . Math.Z., , 82 : 177 – 197 .
- Lazer , A.C. and Solimini , S. 1987 . On periodic solutions of nonlinear differential equations with singularities. . Proc. Amer. Math. Soc. , 99 : 109 – 114 .
- Mawhin , J. 1979 . Topological degreee methods in nonlinear boundary value problems . CBMS Regional Conf.Ser.in Math. , 40
- Mawhin , J. 1993 . “ Topological degree and boundary value problems for nonlinear differential equations. ” . In Topological methods for ordinary differential equations , Edited by: Furi , M. Vol. 1537 , 74 – 142 . New York : Springer-Verlag . Let.Notes Math.
- Mawhin , J. and Wilem , M. 1989 . “ Critical Point Theory and Hamiltonian Systems ” . In Applied Mathematical Sciences , Vol. 74 , Berlin : Springer-Verlag .
- Mitrinovic , D.S. , Pecaric , J.E. and Fink , A.M. 1991 . Involving functions and Their Integrals and Dervatives. . 74
- Omari , P. and Ye , W. 1995 . Necessary and sufficient conditions for the existence of periodic solutions of second order ordinary differential equations with singular nonlinearities . Differential Integral Equations , 8 : 1843 – 1858 .
- Rachůnková , I. 1995 . Existence of two positives solutions of a singular nonliear periodic boundary value problems . J.Comput.Appl.Math., , 113 : 27 – 34 .
- Rachůnková , I. and Tvrdý , M. 2001 . Nonlinear systems of differential inequalities and solvability of certain nonlinear second order boundary value problems . J.Inequal.Appl., , 6 : 199 – 226 .
- Rachůnková , I. and Tvrdý , M. 2000 . Method of lower and upper functions and the existence of solutions to singular periodic problems for second order nonlinear differential equations . Mathematical Notes. Miskolc , 2 : 135 – 143 .
- Rachůnklvá , I. and Tvrdý , M. 2001 . Construction of lower and upper functions and their application to regular and singular periodic boundary value problems . Nonlinear Analysis , 47 : 3937 – 3948 .
- Rachůnklvá I. Tvrdý M. Vrkoc I. Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems J. Differential Eq., to appear.
- Scheeffer , L. 1885 . über die Bedeutung der Begriffe Maximum und Minimum in der variationsrechnung. . Math.Ann., , 56 : 197 – 208 .
- Thompsom , H.T. 1996 . Second order ordinary differtial equations with fully nonliner two point boundary conditions . Pacif.J.Math., , 172 : 255 – 277 .
- Thompson , H.T. 1996 . Second order ordinary differential equations with fully nonlinear two point boundary conditions II . Pacif.J.Math., , 172 : 279 – 297 .
- Vasil'ev N.I. Klokov Yu.A. Foundations of the Theory of Boundary Value Problems for Ordinary Differential Equations Zinatne Riga 1978 (in Russian)
- Zhang , M. 1998 . A relationship between the periodic and the Dirichlet BVP's pf singular differential equations. . Proc.Royol Soc.Edinburgh , 128A : 1099 – 1114 .