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A generalized-degree homotopy yielding global bifurcation results

✍ Scribed by Stewart C. Welsh

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
207 KB
Volume
62
Category
Article
ISSN
0362-546X

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✦ Synopsis

We study the nonlinear eigenvalue problem

is shown that 0 = 0 is a global bifurcation point of the eigenvalue problem provided: a standard transversality condition is satisfied, the dimension of the null space of A is an odd number and each B j , j = 1, 2, . . . , k, is a positive operator on the finite-dimensional null space of A. We apply the theory to prove that = 0 is a global bifurcation point of the periodic boundary-value problem -x (t) + x(t) + 2 x (t) + f (t, x(t), x (t), x (t)); x(0) = x(1), x (0) = x (1).

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