Abstract
Abstract In this paper, under the framework of Ambrosetti [1], using mountain-pass theorem and topological degree theory, we extend the result of Ambrosetti [1] (in which H is independent of λ and C1) to the equation Au + H(λ, u) = λu with H jointly continuous in (λ, u) and H(λ, ·) of class C0, 1. We give a description of the structure of local bifurcation from isolated eigenvalues of A: the set of bifurcation solutions at each isolated eigenvalue of A contains at least one connected branch. Applications to the existence of branching points to semilinear elliptic partial differential equations are given.
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