Electron. J. Differential Equations,
Vol. 2016 (2016), No. 251, pp. 117.
Positive solutions for a secondorder PhiLaplacian equations
with limiting nonlocal boundary conditions
George L. Karakostas, Konstantina G. Palaska, Panagiotis Ch. Tsamatos
Abstract:
Motivated, mainly, by the works of FewsterYoung and Tisdell [9,10]
and Orpel [30], as well as the papers by Karakostas [21,22,23],
we give sufficient conditions to guarantee the existence of (nontrivial)
solutions of the secondorder PhiLaplacian equation
which satisfy the nonlocal boundary value conditions of the
limiting SturmLiouville form
Here
is an increasing homeomorphism of the real line onto itself
and F is an operator acting on the function u and on its first
derivative with the characteristic property that
is a
type, or
type
Caratheodory operator, a meaning introduced here.
Examples are given to illustrate both cases.
Submitted April 19, 2016. Published September 20, 2016.
Math Subject Classifications: 34B18, 34B10.
Key Words: Positive solution; SturmLiouville equation; PhiLaplacian;
Schauder's fixed point theorem.
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George L. Karakostas
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: gkarako@uoi.gr, gkarako@hotmail.com


Konstantina G. Palaska
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: cpalaska@cc.uoi.gr


Panagiotis Ch. Tsamatos
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: ptsamato@cc.uoi.gr

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