Bifurcation of point sources and contour sources of nonlinear fields

The problem of static point sources of a nonlinear scalar field with nonlinearity $\varphi^\nu$ (leading term as $|\varphi|\to\infty$) in a space of dimension $\gamma\geqslant2$ is solved. For $\nu<\nu_c=\gamma/(\gamma-2)$, two different types of point source are found. For $\gamma>2$ when $\nu\geqslant\nu_c$, there are no point sources. In three-dimensional space, contour sources are possible instead of them. The transition from a distributed sources to a point source when the size of the distributed source tends to zero is also considered.