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摘要
For a large class of functions f, we consider the nonlinear biharmonic eigenvalue problem Delta(2)u(x) + f(x, u(x)) = lambda u(x) for x is an element of R-N, lim(vertical bar x vertical bar ->infinity) u(x) = 0, u not equivalent to 0. We describe the behaviour of the branch of solutions emanating from an eigenvalue of odd multiplicity below the essential spectrum of the linearized problem. The discussion is based on the degree theory for C-2 proper Fredholm maps developed by Fitzpatrick, Pejsachowicz and Rabier.
