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

We consider the system of boundary value problems

u1ni(t)+fi(t,u1(t),...,um(t))=0u_1^{n_i}(t)+f_i(t,u_1(t),...,u_m(t))=0
ui(j)(0)=0u_i^{(j)}(0)=0
ui(pi)(1)=0u_i^{(p_i)}(1)=0

for t[0,1],i=1,...,mt \in [0, 1], i = 1, ..., m and 0jnj0 ≤ j ≤ n_j where ni2n_i ≥ 2 and 1pini11 ≤ p_i ≤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