Abstract.
We establish the existence of multiple positive solutions of nonlinear equations of the form
where g, f are non-negative functions, subject to various nonlocal boundary conditions. The common feature is that each can be written as an integral equation, in the space C[0, 1], of the form
where α[u] is a linear functional given by a Stieltjes integral but is not assumed to be positive for all positive u. Our new results cover many non-local boundary conditions previously studied on a case by case basis for particular positive functionals only, for example, many m-point BVPs are special cases. Even for positive functionals our methods give improvements on previous work. Also we allow weaker assumptions on the nonlinear term than were previously imposed.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Webb, J.R.L., Infante, G. Positive solutions of nonlocal boundary value problems involving integral conditions. Nonlinear differ. equ. appl. 15, 45–67 (2008). https://doi.org/10.1007/s00030-007-4067-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00030-007-4067-7