Abstract
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.
Citation
Jan Eisner. Milan Kučera. Lutz Recke. "Smooth bifurcation for variational inequalities based on Lagrange multipliers." Differential Integral Equations 19 (9) 981 - 1000, 2006. https://doi.org/10.57262/die/1356050328
Information