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Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems

Authors:

Wong Patricia J Y Agarwal Ravi P

Institution:

(1) Division of Mathematics, Nanyang Technological University, Singapore

Abstract:

We consider the boundary value problem

$y^{(n)} (t) = P(t,y),{\text{ }}t \in (0,1)$

$y^{(i)} (ti) = 0,{\text{ }}j = 0,...,n_i - 1,{\text{ }}i = 1,...,r,$

where r

2, n _i

1 for i = 1, ... ,r, $\sum {_{i = 1}^r = n}$ and 0 = t ₁ < t ₂ < ... < t _r = 1. Criteria are offered for the existence of double and triple lsquo

positive

(in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for the norms of these solutions is carried out for special cases. We also include several examples to illustrate the importance of the results obtained.

Keywords:

Generalised multipoint conjugate boundary value problem multiple solution

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