The paper deals with the problem of the existence of a branch of T-periodic solutions originating from the isolated limit cycle of an autonomous parabolic equation in a Banach space when it is perturbed by a nonlinear T-periodic term of small amplitude. We solve this problem by first introducing a novel integral operator, whose fixed points are T-periodic solutions of the considered equation and vice versa. Then we compute the Malkin bifurcation function associated to this integral operator and we provide conditions under which the well-known assumption of the existence of a simple zero of the Malkin bifurcation function guarantees the existence of the branch. © 2013 Kamenskii et al.; licensee Springer.
CITATION STYLE
Kamenskii, M., Mikhaylenko, B., & Nistri, P. (2013). A bifurcation problem for a class of periodically perturbed autonomous parabolic equations. Boundary Value Problems, 2013. https://doi.org/10.1186/1687-2770-2013-101
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