A radially symmetric superlinear Dirichlet problem was studied by using the energy analysis and the phase plane analysis.The problem was turned into a boundary value problem of ordinary differential equation.The contraction mapping principle was used to verify the existence of solutions of the differential equation and thereby to prove the existence of infinite radially symmetric solutions.The same result can be still obtained when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem or does not satisfy the Palais Smale condition.Some examples were given to show the advantage of these methods.