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

Kuo, Chung-Cheng

doi:10.1090/S0002-9939-96-03145-0

On the solvability of a nonlinear second-order elliptic equation at resonance
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Proc. Amer. Math. Soc. 124 (1996), 83-87 Request permission

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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