Finitely many solutions for a class of boundary value problems with superlinear convex nonlinearity

We consider the nonlinear Sturm-Liouville problem –u = f(u) + h in (0, 1), u(0) = u(1) = 0, where h L²(0,1) and f is a positive convex nonlinearity with superlinear growth at infinity. Our main result establishes that the above boundary value problem admits a finite number of solutions but it cannot have infinitely many solutions.Received: 8 July 2004