Existence of positive solutions for a class of arbitrary order boundary value problems involving nonlinear functionals
Volume 112 / 2014
Annales Polonici Mathematici 112 (2014), 313-327 MSC: Primary 34K10; Secondary 34B10, 34B15, 34B18, 34B40, 47H10. DOI: 10.4064/ap112-3-8
We give conditions which guarantee the existence of positive solutions for a variety of arbitrary order boundary value problems for which all boundary conditions involve functionals, using the well-known Krasnosel'skiĭ fixed point theorem. The conditions presented here deal with a variety of problems, which correspond to various functionals, in a uniform way. The applicability of the results obtained is demonstrated by a numerical application.