Differential and Integral Equations

Bifurcation for families of nonlinear perturbation of closed Fredholm operators of index zero

Maria Testa

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In this paper we obtain a bifurcation result for parameterized families of $k$ set-contractive perturbations of closed Fredholm operators of index zero by means of an elementary degree theory and its relationship to a homotopy invariant for curves of closed Fredholm operators called the parity. This theorem is applied to the study of bifurcation of nonlinear Sturm Liouville problems on an unbounded interval.

Article information

Differential Integral Equations, Volume 15, Number 11 (2002), 1281-1312.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]
Secondary: 34B15: Nonlinear boundary value problems 34L30: Nonlinear ordinary differential operators 35B32: Bifurcation [See also 37Gxx, 37K50] 47H11: Degree theory [See also 55M25, 58C30] 47N20: Applications to differential and integral equations 58E07: Abstract bifurcation theory


Testa, Maria. Bifurcation for families of nonlinear perturbation of closed Fredholm operators of index zero. Differential Integral Equations 15 (2002), no. 11, 1281--1312. https://projecteuclid.org/euclid.die/1356060722

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