Multiple solutions for an asymptotically linear Duffing equation with Neumann boundary value conditions (Q531672)

Using index theory for linear Duffing equations and Morse theory, the authors obtain multiplicity results for the Neumann boundary value \[ x'' + f(t,x) = 0, \quad x'(0) = 0 = x'(1), \] where \(f\) is of class \(C^1\) and has linear growth. Depending upon the assumptions, they obtain the existence of at least one or at least two solutions.