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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.

electronic journal on the qualitative theory of differential equations

Positive solutions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mi>,</mml:mi> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math>-equations with superlinear reaction and a concave boundary term

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