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) lim u → - ∞ (g(u)/u) ε R
(ii) lim u → ∞ (g(u)/(u1 + ρ )) = ∞ for some ρ > 0, and
(iii) lim u → ∞ (u/g(u))N/2(NG(κ u) - ((N - 2)/2)u · g(u)) = ∞ for some κ ε (0,1] where G is the primitive of g.
Here we prove that the number of solutions of the boundary value problem Δu + g(u) = p(|x|) + cφ (|x|) for x ε RN with |x| < 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
Castro, Alfonso and Kurepa, Alexandra, "Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball with Jumping Nonlinearities" (1989). All HMC Faculty Publications and Research. 465.