Research
Multiplicity of positive solutions for eigenvalue problems of (
p
,
2
)
1 Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. Łojasiewicza 6, Kraków, 30-348, Poland
2 Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece
Boundary Value Problems 2012, 2012:152 doi:10.1186/1687-2770-2012-152
Published: 28 December 2012Abstract
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.
