On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

CSF-1 as a regulator of macrophage activation and immune responses

Macrophage activation is a key determinant of susceptibility and pathology in a variety of inflammatory diseases. The extent of macrophage activation is tightly regulated by a number of pro-inflammatory cytokines (e.g. IFN-gamma, IL-2, GM-CSF, IL-3) and anti-inflammatory cytokines (e.g. IL-4, IL-10, TGF-beta). Macrophage colony-stimulating factor (CSF-1/M-CSF) is a key differentiation, growth and survival factor for monocytes/macrophages and osteoclasts. The role of this factor in regulating macrophage activation is often overlooked. This review will summarize our current understanding of the effects of CSF-1 on the activation state of mature macrophages and its role in regulating immune responses.