Positive solutions for nonlinear nonhomogeneous parametric equations

Nikolaos S. Papageorgiou, George Smyrlis

DOI: http://dx.doi.org/10.12775/TMNA.2015.033

Abstract


We consider a nonlinear parametric Dirichlet problem driven by a nonhomogeneous differential operator which includes as special cases the $p$-Laplacian, the $(p,q)$-Laplacian and the generalized $p$-mean curvature operator. Using variational methods, we prove a bifurcation-type theorem describing the dependence of positive solutions on the parameter.

Keywords


Nonlinear regularity, mountain pass theorem,bifurcation-type theorem, strong comparison principle,nonhomogeneous differential operator, positive solutions

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