Multiple bifurcation branches for variational inequalities

An Efficient Algorithm for Bifurcation Problems of Variational Inequalities

For a class of variational inequalities on a Hubert space H bifurcating solutions exist and may be characterized as critical points of a functional with respect to the intersection of the level surfaces of another functional and a closed convex subset K of H. In a recent paper [13] we have used a gradient-projection type algorithm to obtain the solutions for discretizations of the variational i...

Multiplicity of Bifurcation Points for Variational Inequalities via Conley Index

where K0 = ⋃ t>0 tK is a closed convex cone. The typical problem one has to face is twofold: (1) find eigenvalues (which is nontrivial, unless K0 is a linear space): (2) ensure that some eigenvalues are bifurcation points (which is not always true, as counterexamples show). Much work has been done in this context; see [11], [15]–[18], [21]–[30], [32]–[34] and the references therein for a more c...

Multiple global bifurcation branches for nonlinear Picard problems

In this paper we prove the global bifurcation theorem for the nonlinear Picard problem. The right-hand side function φ is a Caratheodory map, not differentiable at zero, but behaving in the neighbourhood of zero as specified in details below. We prove that in some interval [a, b] ⊂ R the Leray-Schauder degree changes, hence there exists the global bifurcation branch. Later, by means of some app...

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points