Local minimizers over the Nehari manifold for a class of concave-convex problems with sign changing nonlinearity

We study a p-Laplacian equation involving a parameter λ and a concave-convex nonlinearity containing a weight which can change sign. By using the Nehari manifold and the fibering method, we show the existence of two positive solutions on some interval (0,λ⁎+ε), where λ⁎ can be characterized variationally. We also study the asymptotic behavior of solutions when λ↓0.