MULTIPLE SOLUTIONS TO A SINGULAR LANE-EMDEN-FOWLER EQUATION WITH CONVECTION TERM

This article concerns the existence of multiple solutions for the problem -Delta u - K(x)u(-alpha) + s(Au-beta + B vertical bar del u vertical bar(zeta)) + f(x) in Omega u > 0 in Omega u = 0 on partial derivative Omega, where Omega is a smooth, bounded domain in R-n with n >= 2, alpha, beta, zeta, A, B and s are real positive numbers, and f(x) is a positive real valued and measurable function. We start with the case s = 0 and f = 0 by studying the structure of the range of -u(alpha) Delta u. Our method to build K's which give at least two solutions is based on positive and negative principal eigenvalues with weight. For s small positive and for values of the parameters in finite intervals, we find multiplicity via estimates on the bifurcation set.