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| We will consider an asymptotically linear system involving weighted eigenvalue problem.
We provide sufficient conditions for determining the direction of bifurcation of positive and negative solutions from infinity at the first eigenvalue of the associated linear eigenvalue problem. As a corollary to these results, we also provide sufficient conditions for the solvability of a class of asymptotically linear system at resonance satisfying {\it Landesman}--{\it Lazer} type conditions. |
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