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Zeitschrift für Analysis und ihre Anwendungen


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Volume 5, Issue 4, 1986, pp. 347–366
DOI: 10.4171/ZAA/203

Published online: 1986-08-31

Some Applications of Degree Theory to Bifurcation Problems

Nguyen Xuan Tan[1]

(1) Institute of Mathematics, Hanoi, Vietnam

Some results on the vanishing of a generalized degree of multivalued mappings are proved and applied to study bifurcation solutions of the equation $F(\lambda, u) = 0$ in a Banach space; as a special case, $F(\lambda, u) = u—M(u)—N(\lambda, u)—H(\lambda, u)$, where the parameter $\lambda$ is from a normed space. For concrete application there are considered bifurcation solutions of a nonlinear elliptic differential equation of second order.

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Tan Nguyen Xuan: Some Applications of Degree Theory to Bifurcation Problems. Z. Anal. Anwend. 5 (1986), 347-366. doi: 10.4171/ZAA/203