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Bull. Korean Math. Soc. 2014; 51(6): 1669-1687

Printed November 30, 2014

https://doi.org/10.4134/BKMS.2014.51.6.1669

Copyright © The Korean Mathematical Society.

On a Neumann problem at resonance for nonuniformly semilinear elliptic systems in an unbounded domain with nonlinear boundary condition

Hoang Quoc Toan and Bui Quoc Hung

Hanoi University of Science, Le Quy Don Technical University

Abstract

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We consider a nonuniformly nonlinear elliptic systems with resonance part and nonlinear Neumann boundary condition on an unbounded domain. Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition.

Keywords: semilinear elliptic equation, non-uniform, Landesman-Lazer condition, minimum principle

MSC numbers: 35J20, 35J60, 58E05

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