Some global results for nonlinear eigenvalue problems

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Abstract

In this paper we investigate the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space. Our main results demonstrate the existence of continua, i.e., closed connected sets, of solutions of these equations. Although the emphasis is on the case when bifurcation occurs, the nonbifurcation situation is also treated. Applications are given to ordinary and partial differential equations and to integral equations.

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