Multiple solutions for a nonlinear elliptic equation on R^N with nonlinear dependence on the gradient

We are concerned with the existence of L²-solutions of a semilinear elliptic equation on R^N. This problem admits zero as a trivial solution and its linearization about zero has a purely continuous spectrum. When the nonlinearity does not depend on the derivatives of the solutions, the existence of nontrivial solutions has been obtained by various methods. Related questions concerning nontrivial solutions which bifurcate from the line of trivial solutions have also been investigated. However, very little seems to be known for the problem where the nonlinearity does depend on the derivatives of the solutions. The aim of this paper is to use an approximation scheme together with a comparison argument to obtain infinitely many radially symmetric solutions which are distinguished by nodal properties.