Abstract
We consider a nonlinear Dirichlet problem driven by the -Laplacian and with a reaction involving the combined effects of a singular term, of a concave term and of a parametric convex term. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies. Also, we show that for every admissible parameter , the problem has a minimal positive solution and we establish the monotonicity and continuity properties of the map .
2010 Mathematics Subject Classifications:
Acknowledgments
The authors wish to thank a knowledgeable referee for his/her remarks. This work was supported by the National Natural Science Foundation of China (No. 12071098).
Disclosure statement
No potential conflict of interest was reported by the author(s).