Chapter 4 Singular elliptic and parabolic equations

On Very Weak Positive Solutions to Some Semilinear Elliptic Problems With Simultaneous Singular Nonlinear and Spatial Dependence Terms

“…A partial existence result was also found in [17], [16], [18] where, as a particular case of more general results, it was proved directly that the same regularity holds for b > 0 such that a + b < 1, but only for solutions obtained by the method of sub and supersolutions there, and not for any solution. On the other hand, this is shown for general second order differential operators not necessarily in divergence form, and for more complicated singular nonlinearities as well.…”

“…If b < 0, the same argument can be done to recover several results given by [19] and [15] (see also [16]). …”

Existence and regularity results for fully nonlinear equations with singularities

“…In addition to the papers we already quoted we refer to [6], [7], [11], [13], [20], [21], [31], [34], [37], [38] and the references therein. An excellent starting point to these studies is the survey [19], where very extensive literature is available.…”

Nonlinear Elliptic Equations with Singular Terms and Combined Nonlinearities

“…We also mention the work of Giacomoni et al [17] who have a similar result for critical problems in R N . In Hernández and Mancebo [21] we find a comprehensive overview of singular elliptic and parabolic equations. To the best of our knowledge, there are no works in the literature dealing with p-Laplacian equations with singular terms and combined nonlinearities (i.e., with the combined effects of concave and convex terms or of concave and linear terms).…”