Smooth Bifurcation for Variational Inequalities and Reaction-Diffusion Systems

Global bifurcation for quasivariational inequalities of reaction–diffusion type

“…A bifurcation for a problem of the type (6), (3) was studied already in [11]. We generalize this result here in the following…”

New beams of global bifurcation points for a reaction–diffusion system with inequalities or inclusions

“…However, it can happen that a point d 0 The following lemma is an extension of [19,Lemma 2.3]. We carry out the details, because we fix a small gap of the original proof from [19] (the argument for c k > 0 in the following proof needs some additional arguments if n = m which we provide by (4.8)).…”

“…Concerning (1.10)/(1.11), the result was obtained for the case Ω 0 = ∅, f 3 = f 4 = 0, and if f 1 , f 2 are independent of ∇u, ∇ v in various forms of generality in [4,[17][18][19]22] (partially based on a homotopy method developed in [15,16], although we will concentrate about a method involving topological degree); the general case for (1.10)/(1.11) can be obtained along the same lines as [19] under (1.14) resp. as [18] under (1.15).…”

Direction and stability of bifurcation branches for variational inequalities

“…In the present paper as well as in [4,12] (see also [7]), it is essential that our assumptions guarantee that the set of active constraints is constant along the branch of solutions obtained. A generalization of the basic ideas for obtaining smooth bifurcation and continuation in the case of the changing set of active constraints is given in [5,13], but questions of stability are not yet included there.…”