Multiplicity of positive solutions for eigenvalue problems of ( p , 2 ) -equations

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.