Positive solutions for (p, 2)-equations with superlinear reaction and a concave boundary term.

We consider a nonlinear boundary value problem driven by the (p, 2)- Laplacian, with a (p − 1)-superlinear reaction and a parametric concave boundary term (a "concave-convex" problem). Using variational tools (critical point theory) together with truncation and comparison techniques, we prove a bifurcation type theorem describing the changes in the set of positive solutions as the parameter λ > 0 varies. We also show that for every admissible parameter λ > 0, the problem has a minimal positive solution uλ and determine the monotonicity and continuity properties of the map λ 7→ uλ. [ABSTRACT FROM AUTHOR]