Branching Point For A Class Of Varational Equation Involving Potential With Parameter

In this paper, under the framework of Ambrosetti [1], using mountain-pass theorem and topological degree theory, we extend the result of Ambrosetti to equations Au＋H(λ,u)=λu with H jointly continuous in (λ, u) and H(λ,.) of class C^0,1. We give a description of the structure of local bifurcation from isolated eigenvaiues 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 problems are given.