Discrete Higher Order Sturm-Liouville Boundary Value Problems

Ravi P. Agarwal, Donal O’Regan and Patricia J. Y. Wong
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Ravi P. Agarwal: National University of Singapore, Department of Mathematics
Donal O’Regan: National University of Ireland, Department of Mathematics
Patricia J. Y. Wong: Nanyang Technological University, Division of Mathematics

Chapter Chapter 18 in Positive Solutions of Differential, Difference and Integral Equations, 1999, pp 279-314 from Springer

Abstract: Abstract In this chapter we shall obtain results which are mainly analogous to those obtained in Chapter 12 for the discrete boundary value problem 18.1 $${\Delta ^n}y + \lambda Q\left( {k,y,\Delta y, \cdots ,{\Delta ^{n - 2}}y} \right) = \lambda P\left( {k,y,\Delta y, \cdots ,{\Delta ^{n - 1}}y} \right),k \in \left[ {0,T} \right]$$ 18.2 $$ {\Delta ^i}y\left( 0 \right) = 0,0 \leqslant i \leqslant n - 3 $$ 18.3 $$\alpha {\Delta ^{n - 2}}y\left( 0 \right) - \beta {\Delta ^{n - 1}}y\left( 0 \right) = 0$$ 18.4 $$\gamma {\Delta ^{n - 2}}y\left( {T + 1} \right) + \delta {\Delta ^{n - 1}}y\left( {T + 1} \right) = 0$$ .

Date: 1999
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DOI: 10.1007/978-94-015-9171-3_18

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