Quinn A. Morris, Stephen B. Robinson
Abstract:
In this article we prove the existence of solutions for the
boundary-value 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 Landesman-Lazer
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; Landesman-Lazer 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 Winston-Salem, NC 27109, USA email: sbr@wfu.edu |
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