This paper deals with the existence of multiple solutions for some cla
sses of nonlinear elliptic Dirichlet boundary value problems. The inte
rplay of convex and concave nonlinearities is studied both for second
order equations and for problems involving the p-laplacian. The bifurc
ation of positive solutions for some quasilinear eigenvalue problems i
s also discussed. (C) 1996 Academic Press, Inc.