George L. Karakostas, Konstantina G. Palaska, Panagiotis Ch. Tsamatos
Abstract:
Motivated, mainly, by the works of Fewster-Young 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 second-order Phi-Laplacian equation
which satisfy the nonlocal boundary value conditions of the
limiting Sturm-Liouville 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; Sturm-Liouville equation; Phi-Laplacian;
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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