EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N)

We study the semilinear elliptic PDE -Delta u + b(x)u = f(x, u) in R(N). The nonlinearity f will be superlinear and subcritical. We prove the existence of a positive solution under various hypotheses on b. If b(x) = lambda alpha(x)+1 and f is odd in u, then we also discuss the dependence of the number of (possibly sign changing) solutions on the parameter lambda. We do not assume that b or f have a limit for \x\ --> infinity.