Lagrange Mulitpliers and Lower Bounds for Integral Functionals

We present a large class of examples with the remarkable property pointed out by B. Ricceri in "A variational property of integral functionals on Lp spaces of vector-valued functions" [C. R. Acad. Sci. Paris, Série I Math. 318 (1994) 337--342], "More on a variational property of integral functionals" [J. Optimisation Theory Appl. 94 (1997) 757--763], and in "Further considerations on a variational property of integral functionals" [J. Optimisation Theory Appl. 106 (2000) 677--681], about lower bounds of integral functionals. We use only a Lagrange duality result of A. Bourass and E. Giner [see: "Kuhn-Tucker conditions and integral functionals", J. Convex Analysis 8 (2001) 533--553].