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

By K. Silva, A. Macedo. Journal of Differential Equations, 2017

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Abstract 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 ⁎ + e ) , where λ ⁎ can be characterized variationally. We also study the asymptotic behavior of solutions when λ ↓ 0 .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

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