Abstract :
For any integer m 2, we consider the 2mth order boundary value problem
(−1)mu(2m)(x) = λg u(x) u(x), x ∈ (−1, 1),
u(i)(−1) = u(i)(1) = 0, i= 0, . . . , m − 1,
where λ ∈ R, and the function g :R→R is C1 and satisfies
g(0) > 0, ±g (ξ ) > 0, ±ξ >0,
together with some further conditions as |ξ|→∞. We obtain curves of nontrivial solutions of this
problem, bifurcating from u = 0 at the eigenvalues of the linearised problem, and obtain the exact
number of solutions of the problem for λ lying in various intervals in R.
2003 Elsevier Inc. All rights reserved
