On a singular Robin problem with convection terms

TL;DR

This paper establishes the existence and uniqueness of smooth positive solutions for a Robin boundary-value problem involving a nonlinear convection term and a singular reaction, using advanced mathematical techniques.

Contribution

It introduces new existence and uniqueness results for a Robin problem with complex nonlinear and singular terms, employing innovative analytical methods.

Findings

Existence of smooth positive solutions is proven.

Uniqueness of solutions is established.

The methods can handle non-homogeneous operators with convection and singular reactions.

Abstract

In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly exploit sub-super-solution and truncation techniques, set-valued analysis, recursive methods, nonlinear regularity theory, as well as fixed point arguments. A uniqueness result is also presented.