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Constant-Sign Solutions of Systems of Integral Equations pp 231–269Cite as

Systems of Higher Order Boundary Value Problems: Integrable Singularities

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Abstract

In this chapter we shall consider three systems of boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. The first system we tackle is that of Dirichlet boundary value problems

$$\displaystyle{\left\{\begin{array}{l} v^{\prime \prime}_{i}(t) + f_{i}(t,\tilde{v}(t)) = 0,\ \ a.e.\ t \in [0,1] \\ v_{i}(0) = v_{i}(1) = 0, \\ i = 1,2,\cdots \,,n\end{array} \right. }$$
(8.1.1)

where

$$\displaystyle{\tilde{v} \equiv (v_{1},v^{\prime}_{1},v_{2},v^{\prime}_{2}\cdots \,,v_{n},v^{\prime}_{n}).}$$

The nonlinearities f i , 1 ≤ i ≤ n in the above system may be singular in the independent variable and may also be singular at v i = 0 where \(i \in \{ 1,2,\cdots \,,n\}.\)

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University – Kingsville, Kingsville, TX, USA

    Ravi P. Agarwal

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Galway, Ireland

    Donal O’Regan

  3. School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Patricia J. Y. Wong

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  1. Ravi P. Agarwal
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  2. Donal O’Regan
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  3. Patricia J. Y. Wong
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Agarwal, R.P., O’Regan, D., Wong, P.J.Y. (2013). Systems of Higher Order Boundary Value Problems: Integrable Singularities. In: Constant-Sign Solutions of Systems of Integral Equations. Springer, Cham. https://doi.org/10.1007/978-3-319-01255-1_8

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