Existence of Positive Weak Solutions for Quasi-Linear Kirchhoff Elliptic Systems via Sub-Supersolutions Concept

Abstract

By using the sub- and supersolutions concept (Schmitt, 2007), we prove in this paper the existence of positive solutions of quasi-linear Kirchhoff elliptic systems in bounded smooth domains. This work is an extension of the recent work of Boulaaras et al., 2020.

Further results of existence of positive solutions of elliptic Kirchhoff equation with general nonlinearity of source terms

“…where we used the subsolution-supersolution method (see previous studies [7][8][9][10][11][12][13][14][15][16][17][18] ), Galerkin approach, and a variational method to prove the existence of positive solutions in different cases depending on the parameters p and . We chose the logarithmic nonlinearity of source terms, because it appears in several branches of physics such as inflationary cosmology, nuclear physics, optics, and geophysics (see previous studies 2,4,12,[19][20][21][22][23] ).…”

Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem

“…The approach employed in [14] is the sub-supersolution method. The system (1.3) has been studied also by the sub-supersolution method in [8,35,6,7], while variational methods were employed in [19,32,38,49].…”