Geodesic
Method of guiding functions for existence problems for periodic solutions of differential equations
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 59-81

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We provide a review and systematic explanation of various generalizations of the guiding function method. The current state of the said method and its applications to various kinds of problems for nonlinear periodic systems described by differential and functional differential equations are considered. 
@article{CMFD_2015_58_a3,
     author = {V. G. Zvyagin and S. V. Kornev},
     title = {Method of guiding functions for existence problems for periodic solutions of differential equations},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {59--81},
     publisher = {mathdoc},
     volume = {58},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2015_58_a3/}
}
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V. G. Zvyagin; S. V. Kornev. Method of guiding functions for existence problems for periodic solutions of differential equations. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 59-81. http://geodesic.mathdoc.fr/item/CMFD_2015_58_a3/