Multiple Solutions for a System of $(n_i, p_i)$  Boundary Value Problems

Patricia J.Y. Wong; R.P. Agarwal

doi:10.4171/zaa/964

JournalszaaVol. 19, No. 2pp. 511–528

Multiple Solutions for a System of $(n_{i}, p_{i})$ Boundary Value Problems

Patricia J.Y. Wong
Nanyang Technological University, Singapore, Singapore
R.P. Agarwal
National University of Singapore, Singapore

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Abstract

We consider the system of boundary value problems

u_{1}^{n_{i}} (t) + f_{i} (t, u_{1} (t), ..., u_{m} (t)) = 0 u_{i}^{(j)} (0) = 0 u_{i}^{(p_{i})} (1) = 0 ⎭ ⎬ ⎫

for $t \in [0, 1], i = 1, ..., m$ and $0 \leq j \leq n_{i} - 2$ where $n_{i} \geq 2$ and $1 \leq p_{i} \leq n_{i} -1$ . Several criteria are offered for the existence of single and twin solutions of the system that are of fixed signs.

Cite this article

Patricia J.Y. Wong, R.P. Agarwal, Multiple Solutions for a System of $(n_{i}, p_{i})$ Boundary Value Problems. Z. Anal. Anwend. 19 (2000), no. 2, pp. 511–528

DOI 10.4171/ZAA/964