Global solution branches for equations involving nonhomogeneous operators of pp-Laplace type

It is shown that if μμ is not an eigenvalue of an associated pp-Laplacian, then the equation View the MathML source−div(φ(x,∇u))=μ|u|p−2u+f(λ,x,u,∇u) Turn MathJax on with nonhomogeneous φφ (which is assumed to behave asymptotically as the function generating the associated pp-Laplacian) has a global branch of solutions (λ,u)(λ,u). Also the case of modified pp-Laplace operators and generalizations thereof are discussed.