Geodesic
Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 52-63

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We prove a theorem on the unique existence of a solution to a nonlinear equation with maxima and demonstrate its continuous dependence on the initial function and the parameter of the problem. We also establish conditions for the existence of a nonzero solution to a two-point boundary-value periodic problem in dependence of both linear and nonlinear terms of the equation.
Keywords: initial function, parameter, compact, equation with maxima, two-point boundary-value periodic problem, fundamental matrix, operator, fixed point, admissible vector of a matrix.
Mots-clés : theorem on the unique existence of a solution 
@article{IVM_2010_6_a5,
     author = {M. T. Teryokhin and V. V. Kiryushkin},
     title = {Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--63},
     publisher = {mathdoc},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_6_a5/}
}
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M. T. Teryokhin; V. V. Kiryushkin. Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 52-63. http://geodesic.mathdoc.fr/item/IVM_2010_6_a5/