Positive Solutions for Some Indefinite Nonlinear Eigenvalue Elliptic Problems with Robin Boundary Conditions

We consider a nonlinear eigenvalue problem with indefinite weight under Robin boundary conditions. We prove the existence and multiplicity of positive solutions. To this end, we carry out a detailed study of some linear eigenvalues problems and we use mainly bifurcation and sub-supersolution methods. © 2014 Elsevier Ltd.