Positive solutions for parametric nonlinear neumann problems with competing nonlinearities
We consider a parametric nonlinear Neumann problem driven by the p-Laplacian and with a reaction exhibiting the competing effects of a concave (p-sublinear) and of a convex (p-superlinear) term. Using critical point theory together with truncation and comparison techniques, we prove a bifurcation type theorem describing the set of positive solutions as the parameter λ > 0 varies.
Bifurcations, Concave-convex nonlinearity, Non-linear maximum principle, Nonlinear regularity, Positive solution
Hou, Chunjuan, Shouchuan Hu, and N. S. Papageorgiou. "Positive solutions for parametric nonlinear neumann problems with competing nonlinearities." Houston Journal of Mathematics 41, no. 3 (2015): 993-1019.
Houston Journal of Mathematics