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In this paper, we are interested in looking for multiple solutions for a class of Kirchhoff type problems with concave-convex nonlinearities. Under the combined effect of coefficient functions of concave-convex nonlinearities, by the Nehari method, we obtain two solutions, and one of them is a ground state solution. Under some stronger conditions, we point that the two solutions are positive solutions by the strong maximum principle.2000 Mathematics Subject Classification. Primary: 35J25; Secondary: 35B50.

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Using the minimax methods in critical point theory and a generalized Landesman-Lazer type condition, we establish two existence results of solutions for asymptotically linear noncooperative elliptic systems at resonance. Besides this, we obtain two solutions in the case of near resonance.