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PATRICK FITZPATRICK AND JACOBO PEJSACHOWICZ
when u = u and | i = 0, (DEVP) has only trivial solutions, then
ind(F,uQ) = (-l)m,
where m is the sum, over JI 0, of the multiplicities of (DEVP) at
U = UQ.
We note that in the case when k = 1 and the boundary condition is
u = 0 on 8Q, in [Li], Yan Yan Li modified our construction in [Fi-Pe,l]
to also develop a homotopy invariant degree theory for (DBVP).
For families of (DBVP)'s parametrized by R, if u = 0 is a solution
for all A, there is global bifurcation of nontrivial solutions from
[a,b] x {0} provided that ind(F (0)) * ind(Fw(0)), and the index is
a b
computed as above in terms of the multiplicities of the eigenvalue problem
(DEVP).
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