The sub-supersolution method for variable exponent double phase systems with nonlinear boundary conditions

Abstract

In this paper we study quasilinear elliptic systems driven by variable exponent double phase operators involving fully coupled right-hand sides and nonlinear boundary conditions. The aim of our work is to establish an enclosure and existence result for such systems by means of trapping regions formed by pairs of sup-and supersolutions. Under very general assumptions on the data we then apply our result to get infinitely many solutions. Moreover, we also discuss the case when we have homogeneous Dirichlet boundary conditions and present some existence results for this kind of problem.

Existence of weak solutions for Kirchhoff type double‐phase problem in ℝ

“…They also obtained an existence result for a problem involving a convection term. For some more existence results, we refer to the works of Aberqi et al [16] (a problem on complete manifold), Kim et al [17] (convex-concave nonlinearities), Guarnotta et al [18] (system with convection term), Vetro and Winkert [19], Arora and Dwivedi [20] (singular nonlinearity), and Ho and Winkert [21] (for Kirchhoff type) and Ho and Winkert [22](embedding results and a priori bounds).…”