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Existence and uniqueness for second-order vector boundary value problem of nonlinear systems

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Abstract

This paper is concerned with the following second-order vector boundary value problem: x″ =f(t,Sx,x,x′), 0<t<1, x(0)=A, g(x(1), x′(1))=B, where x, f, g, A and B are n-vectors. Under appropriate assumptions, existence and uniqueness of solutions are obtained by using upper and lower solutions method.

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Authors and Affiliations

  1. Dept. of Math., Beijing Institute of Technology, 100081, Beijing, China

    Du Zengji & Ge Weigao

  2. Dept. of Math., Xuzhou Normal Univ., 221116, Xuzhou, China

    Lin Xiaojie

Authors
  1. Du Zengji
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  2. Lin Xiaojie
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  3. Ge Weigao
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Additional information

Supported by the National Natural Science Foundation of China (10371006) and the Doctoral Program Foundation of Education Ministry of China.

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Zengji, D., Xiaojie, L. & Weigao, G. Existence and uniqueness for second-order vector boundary value problem of nonlinear systems. Appl. Math. Chin. Univ. 20, 323–330 (2005). https://doi.org/10.1007/s11766-005-0008-6

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  • DOI: https://doi.org/10.1007/s11766-005-0008-6

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