Multiplicity of positive solutions for eigenvalue problems of
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Boundary Value Problems 2012, 2012:152 doi:10.1186/1687-2770-2012-152Published: 28 December 2012
We consider a nonlinear parametric equation driven by the sum of a p-Laplacian () and a Laplacian (a -equation) with a Carathéodory reaction, which is strictly -sublinear near +∞. Using variational methods coupled with truncation and comparison techniques, we prove a bifurcation-type theorem for the nonlinear eigenvalue problem. So, we show that there is a critical parameter value such that for the problem has at least two positive solutions, if , then the problem has at least one positive solution and for , it has no positive solutions.
MSC: 35J25, 35J92.