Vol. 57, No. 2, 1975

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Bifurcation of operator equations with unbounded linearized part

David Westreich

Vol. 57 (1975), No. 2, 611–618
Abstract

The bifuraction problem for the operator equation x = λLx + G(λ,x) is considered, where L is a closed linear operator with characteristic value λ0, and G(λ,x) is a continuous higher order term. If I λ0L is a closed Fredholm operator and either L is self-adjoint and G is a continuously differentiable gradient operator or λ0 is of odd algebraic multiplicity, then λ0 is shown to be a bifurcation point.

Mathematical Subject Classification
Primary: 47H15
Milestones
Received: 12 April 1974
Revised: 21 February 1975
Published: 1 April 1975
Authors
David Westreich