Nonhomogeneous systems involving critical or subcritical nonlinearities

TL;DR

This paper proves the existence of positive solutions for nonhomogeneous systems with critical or subcritical nonlinearities, using minimization techniques and energy considerations, under smallness conditions on the nonhomogeneous terms.

Contribution

It introduces a new approach to establish positive solutions in nonhomogeneous systems with critical/subcritical nonlinearities via energy minimization.

Findings

Existence of positive solutions under small nonhomogeneous terms

Solutions have negative energy levels

Applicable to systems with critical/subcritical nonlinearities

Abstract

This paper deals with existence of a nontrivial positive solution to systems of equations involving nontrivial nonhomogeneous terms and critical or subcritical nonlinearities. Via a minimization argument we prove existence of a positive solution whose energy is negative provided that the nonhomogeneous terms are small enough in the dual norm.