Electron. J. Diff. Eqns., Vol. 2002(2002), No. 46, pp. 1-15.
### Positive solutions for a nonlocal boundary-value problem
with vector-valued response

Andrzej Nowakowski & Aleksandra Orpel

**Abstract:**

Using variational methods, we study the existence of positive
solutions for a nonlocal boundary-value problem with vector-valued
response. We develop duality and variational principles for this
problem and present a numerical version which enables the
approximation of solutions and gives a measure of a duality gap
between primal and dual functional for approximate solutions
for this problem.
Submitted February 27, 2002. Published May 28, 2002.

Math Subject Classifications: 34B18.

Key Words: Nonlocal boundary-value problems, positive
solutions, duality method, variational method.

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Andrzej Nowakowski

Faculty of Mathematics, University of Lodz,

Banacha 22, 90-238 Lodz, Poland

e-mail: annowako@math.uni.lodz.pl
Aleksandra Orpel

Faculty of Mathematics, University of Lodz,

Banacha 22, 90-238 Lodz, Poland

e-mail: orpela@math.uni.lodz.pl

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