Location of solutions for quasi-linear elliptic equations with general gradient dependence

Abstract

Existence and location of solutions to a Dirichlet problem driven by $(p,q)$-Laplacian and containing a (convection) term fully depending on the solution and its gradient are established through the method of subsolution-supersolution. Here we substantially improve the growth condition used in preceding works. The abstract theorem is applied to get a new result for existence of positive solutions with a priori estimates.

Keywords

• quasi-linear elliptic equations
• gradient dependence
• $(p
• q)$-laplacian
• subsolution-supersolution
• positive solution