Positive solutions for a nonlocal boundary-value problem with vector-valued response

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.

Keywords

• Nonlocal boundary-value problems
• positive solutions
• duality method
• variational method.