Applications of Sub-Supersolution Theorems to Singular Nonlinear Elliptic Problems

The results presented here were motivated by several recent papers on singular boundary value problems for semilinear elliptic equations with convection terms. We present extensions which cover singular nonlinear equations (mainly equations involving the p−Laplacian) containing convection terms. The results obtained are proved using sub- and supersolution theorems (motivated by the results in [18, 19, 20, 23]) and the construction of a well-ordered pair of such using a principal eigenfunction of the p−Laplacian.

Singular nonlinear elliptic equations inRn

This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the form−Δu+a(x)u=h(x)u−γinRnwherea,hare given, not necessarily continuous functions, andγis a positive number. We explore both situations wherea,hare radial functions, withabeing eventually identically zero, and cases where no symmetry is required from eitheraorh. Schauder's fixed point theorem, combined with penalty arguments, is exploited.