On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

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.