Ninth MSUUAB Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 20 (2013), pp. 103117.
A LandesmanLazer condition for the boundaryvalue problem
with periodic boundary conditions
Quinn A. Morris, Stephen B. Robinson
Abstract:
In this article we prove the existence of solutions for the
boundaryvalue problem
where
,
,
,
and
is a bounded, continuous function. We consider both the resonance
and nonresonance cases relative to the Fucik Spectrum.
For the resonance case we assume a generalized LandesmanLazer
condition that depends upon the average values of g at
.
Our theorems generalize the results in [1] by removing
certain restrictions on (a,b). Our proofs are also different in
that they rely heavily on a variational characterization of
the Fucik Spectrum given in [3].
Published October 31, 2013.
Math Subject Classifications: 34B15.
Key Words: Fucik spectrum; resonance; LandesmanLazer condition;
variational approach.
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Quinn A. Morris
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
116 Petty Building, 317 College Avenue
Greensboro, NC 27412, USA
email: qamorris@uncg.edu


Stephen B. Robinson
Department of Mathematics, Wake Forest University
PO Box 7388, 127 Manchester Hall
WinstonSalem, NC 27109, USA
email: sbr@wfu.edu

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