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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the solvability of a nonlinear
second-order elliptic equation at resonance

Author: Chung-Cheng Kuo
Journal: Proc. Amer. Math. Soc. 124 (1996), 83-87
MSC (1991): Primary 35J65, 47H11, 47H15
MathSciNet review: 1301035
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Abstract: We study the existence of solutions of the Neumann problem for semilinear second-order elliptic equations at resonance in which the nonlinear terms may grow superlinearly in one of the directions $u\to\infty$ and $u\to-\infty$, and sublinearly in the other. Solvability results are obtained under assumptions either with or without a Landesman-Lazer condition. The proofs are based on degree-theoretic arguments.

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Additional Information

PII: S 0002-9939(96)03145-0
Keywords: Second-order elliptic equation, Landesman-Lazer condition, Leray-Schauder degree
Received by editor(s): June 8, 1994
Additional Notes: This research was supported in part by the National Science Council of the Republic of China
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1996 American Mathematical Society