Multiplicity of solutions to the following boundary value problem -(φ(u'))' = λψ(u), T < x < T; u(-T) = u(T) = 0, is considered. There are many works devoted to odd function φ, ψ, but are very few on non-odd cases. For the prototype function φ(u) = au^p, u >0, = -b |u|^q,u < 0 several exact multiplicity results have been established.