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 12 in Positive Solutions of Differential, Difference and Integral Equations, 1999, pp 131-189 from Springer

Abstract: Abstract In this chapter we shall provide sufficient conditions so that the boundary value problem 12.1 $${y^{(n)}} + \lambda Q(t,y,y',...,{y^{(q1)}}) = \lambda p(t,y,y',...,{y^{({q_2})}}),0 0, 0 ≤ q l, q 2 ≤ n-2 but fixed, and the constants α, β, γ, δ are such that 12.5 $$\rho = \alpha \gamma + \alpha \delta + \beta \gamma > 0$$ and 12.6 $$\beta \geqslant 0,\,\delta \geqslant 0,\,\beta + \alpha > 0,\,\delta + \gamma > 0.$$

Keywords: Banach Space; Ordinary Differential Equation; Fixed Point Theorem; Successive Integration; Compact Mapping (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-94-015-9171-3_12

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