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On boundary value problems for systems of nonlinear generalized ordinary differential equations

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Abstract

A general theorem (principle of a priori boundedness) on solvability of the boundary value problem dx = dA(t) · f(t, x), h(x) = 0 is established, where f: [a, b]×Rn → Rn is a vector-function belonging to the Carathéodory class corresponding to the matrix-function A: [a, b] → Rn×n with bounded total variation components, and h: BVs([a, b],Rn) → Rn is a continuous operator. Basing on the mentioned principle of a priori boundedness, effective criteria are obtained for the solvability of the system under the condition x(t1(x)) = B(x) · x(t 2(x))+c 0, where t i: BVs([a, b],Rn) → [a, b] (i = 1, 2) and B: BVs([a, b], Rn) → Rn are continuous operators, and c 0 ∈ Rn.

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Authors and Affiliations

  1. A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili St., Tbilisi, 0177, Georgia

    Malkhaz Ashordia

  2. Sukhumi State University, 12, Politkovskaya St., Tbilisi, 0186, Georgia

    Malkhaz Ashordia

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  1. Malkhaz Ashordia
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Correspondence to Malkhaz Ashordia.

Additional information

This work is supported by the Shota Rustaveli National Science Foundation (Grant No. GNSF/ST09-175-3-101).

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Ashordia, M. On boundary value problems for systems of nonlinear generalized ordinary differential equations. Czech Math J 67, 579–608 (2017). https://doi.org/10.21136/CMJ.2017.0144-11

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  • DOI: https://doi.org/10.21136/CMJ.2017.0144-11

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