Quinn A. Morris, Stephen B. Robinson
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  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 .
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
| Stephen B. Robinson |
Department of Mathematics, Wake Forest University
PO Box 7388, 127 Manchester Hall
Winston-Salem, NC 27109, USA
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