Zuev, A. V. Boundary-value problems with nonlinear conditions for an ordinary differential equation with discontinuous right-hand part. (Russian, English) Zbl 1124.34314 Vestn. Mosk. Univ., Ser. I 2006, No. 2, 23-29 (2006); translation in Mosc. Univ. Math. Bull. 61, No. 2, 24-29 (2006). A new version of the method of shift along trajectories which does not require uniqueness of solution to the Cauchy problem is applied to prove a theorem on the existence of a solution to several boundary-value problems with nonlinear conditions for a vector ordinary differential equation of first and second order. The obtained result is applicable to equations with discontinuous right-hand part and to differential inclusions. Reviewer: Anatoly Martynyuk (Kyïv) MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34A36 Discontinuous ordinary differential equations 34A60 Ordinary differential inclusions Keywords:boundary-value problem; method of shift along trajectory PDFBibTeX XMLCite \textit{A. V. Zuev}, Vestn. Mosk. Univ., Ser. I 2006, No. 2, 23--29 (2006; Zbl 1124.34314); translation in Mosc. Univ. Math. Bull. 61, No. 2, 24--29 (2006)