Radially symmetric solutions to a superlinear dirichlet problem in a ball with jumping nonlinearities

Let p, φ: [0, T] → R be bounded functions with φ > 0. Let g: R → R be a locally Lipschitzian function satisfying the superlinear jumping condition: (i) limu→-∞(g(u)/u) ε R, (ii) lim→∞(g(u)/ul+f) = ∞ forsome ρ > 0, and (iii) lim→∞(u/g(u))Nl/2(NG(Ku) - ((N - 2)/2)u g(u)) = ∞ for some k ε (0, 1] where G is the primitive of g. Here we prove that the number of solutions of the boundary value problem ∆u + g(u) = p(x) + cφ(x) for x ε RNwith;c = T, u(x) = 0 for x = T, tends to +∞ when c tends to +∞. The proofs are based on the "energy" and "phase plane" analysis. © 1989 American Mathematical Society.