Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 71, pp. 117.
Existence of solutions for an ndimensional operator equation and
applications to BVPs
George L. Karakostas
Abstract:
By applying the GuoLakshmikantham fixed point theorem on high
dimensional cones, sufficient conditions are given to guarantee the
existence of positive solutions of a system of equations of the form
Applications are given to three boundary value problems: A
3dimensional 3+3+3 order boundary value problem with mixed nonlocal
boundary conditions, a 2dimensional 2+4 order nonlocal boundary
value problem discussed in [14], and a 2dimensional 2+2 order
nonlocal boundary value problem discussed in [35]. In the latter
case we provide some fairly simpler conditions according to those
imposed in [35].
Submitted February 19, 2014. Published March 16, 2014.
Math Subject Classifications: 34B10, 34K10.
Key Words: Krasnoselskii's fixed point theorem; highdimensional cones;
nonlocal and multipoint boundary value problems;
system of differential equations.
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George L. Karakostas
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: gkarako@uoi.gr

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