Strongly singular convective elliptic equations in RN driven by a non-homogeneous operator

TL;DR

This paper proves the existence of solutions for strongly singular convective elliptic equations in RN with non-homogeneous operators, using advanced mathematical techniques like fixed point theory and variational methods.

Contribution

It introduces a novel approach to handle non-homogeneous (p,q)-Laplacian type operators in singular elliptic equations in the whole space.

Findings

Existence of generalized solutions established.

Applicable to non-homogeneous differential operators.

Utilizes fixed point, variational, and regularity theories.

Abstract

Existence of a generalized solution to a strongly singular convective elliptic equation in the whole space is established. The differential operator, patterned after the (p,q)-Laplacian, can be non-homogeneous. The result is obtained by solving some regularized problems through fixed point theory, variational methods and compactness results, besides exploiting nonlinear regularity theory and comparison principles.