NEUMANN PROBLEMS WITH DOUBLE RESONANCE

We study elliptic Neumann problems in which the reaction term at infinity is resonant with respect to any pair {(lambda) over cap (m),(lambda) over cap (m)+1} of distinct consecutive eigenvalues. Using variational methods combined with Morse theoretic techniques, we show that when the double resonance occurs in a nonprincipal spectral interval [(lambda) over cap (m),(lambda) over cap (m)+1], m = 1, we have at least three nontrivial smooth solutions, two of which have constant sign. If the double resonance occurs in the principal spectral [(lambda) over cap (0) = 0,(lambda) over cap (1)], then we show that the problem has at least one nontrivial smooth solution.