Bifurcation of operator equations with unbounded linearized part

David Westreich

Vol. 57 (1975), No. 2, 611–618

DOI: 10.2140/pjm.1975.57.611

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