Document Type: Research Paper

**Authors**

^{1}
Faculty of Information Technology, Le Quy Don Technical University, 236 Hoang Quoc Viet, Bac Tu Liem, Hanoi, Vietnam.

^{2}
Department of Mathematics, Hanoi University of Science 334 Nguyen Trai, Thanh Xuan, Ha Noi, Vietnam.

**Abstract**

This article shows the existence of weak solutions of a resonance problem for nonuniformly p-Laplacian system in a bounded domain in $\mathbb{R}^N$. Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition.

**Keywords**

**Main Subjects**

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Volume 43, Issue 5

September and October 2017

Pages 1511-1528

**Receive Date:**28 February 2016**Revise Date:**13 July 2016**Accept Date:**14 July 2016