Differential and Integral Equations

Smooth bifurcation for variational inequalities based on Lagrange multipliers

Jan Eisner, Milan Kučera, and Lutz Recke

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We prove a bifurcation theorem of Crandall-Rabinowitz type (local bifurcation of smooth families of nontrivial solutions) for general variational inequalities on possibly nonconvex sets with infinite-dimensional bifurcation parameter. The result is based on local equivalence of the inequality to a smooth equation with Lagrange multipliers, on scaling techniques and on an application of the implicit function theorem. As an example, we consider a semilinear elliptic PDE with nonconvex unilateral integral conditions on the boundary of the domain.

Article information

Differential Integral Equations, Volume 19, Number 9 (2006), 981-1000.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J85
Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09] 49J40: Variational methods including variational inequalities [See also 47J20]


Eisner, Jan; Kučera, Milan; Recke, Lutz. Smooth bifurcation for variational inequalities based on Lagrange multipliers. Differential Integral Equations 19 (2006), no. 9, 981--1000. https://projecteuclid.org/euclid.die/1356050328

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