Systems of Higher Order Boundary Value Problems: Integrable Singularities

Ravi P. Agarwal, Donal O’Regan and Patricia J. Y. Wong
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Ravi P. Agarwal: Texas A&M University – Kingsville, Department of Mathematics
Donal O’Regan: National University of Ireland, Galway, School of Mathematics, Statistics and Applied Mathematics
Patricia J. Y. Wong: Nanyang Technological University, School of Electrical & Electronic Engineering

Chapter Chapter 8 in Constant-Sign Solutions of Systems of Integral Equations, 2013, pp 231-269 from Springer

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

Keywords: Higher Order Boundary Value Problems; Dependence Argument; Nonlinearity; Constant Sign Solutions; Present Existence Results (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01255-1_8

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DOI: 10.1007/978-3-319-01255-1_8

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