Uniqueness of {\sigma}-regular solutions of quasilinear elliptic problems

TL;DR

This paper investigates the uniqueness of ta-regular solutions to certain quasilinear elliptic equations, including mean curvature and subelliptic operators, extending known results to broader classes of differential operators.

Contribution

It establishes new uniqueness results for ta-regular solutions of quasilinear elliptic equations involving various differential operators, including mean curvature and subelliptic types.

Findings

Uniqueness results for ta-regular solutions of specific elliptic equations.

Extension of uniqueness to mean curvature and subelliptic operators.

Applicability to a broader class of coercive differential equations.

Abstract

We study the uniqueness problem of $\sigma$-regular solution of the equation, $$-\Delta_p u+ \abs u^{q-1}u =h \quad on\quad \RN, $$ where $q>p-1>0.$ and $N> p.$ Other coercive type equations associated to more general differential operators are also investigated. Our uniqueness results hold for equations associated to the mean curvature type operators as well as for more general quasilinear subelliptic operators.