Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane-Emden-Fowler type

We are concerned with the generalized Lane-Emden-Fowler equation -Delta u = lambda f (u) + a(x)g(u) in Omega, subject to the Dirichlet boundary condition u vertical bar(theta Omega) = 0, where Omega is a smooth bounded domain in R-N, lambda is an element of R, a is a nonnegative Holder function, and f is positive and nondecreasing such that the mapping f (s)/s is nonincreasing in (0, infinity). Here, the singular character of the problem is given by the nonlinearity g which is assumed to be unbounded around the origin. We distinguish two different cases which are related to the sublinear (respectively linear) growth of f at infinity. (c) 2004 Elsevier SAS. All rights reserved.