Existence of positive weak solutions for a class of Kirrchoff elliptic systems with multiple parameters

Abstract

In this paper, by using subsuper solutions method, we study the existence of weak positive solution for a class of Kirrchoff elliptic systems in bounded domains with multiple parameters.

Some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity

“…Our results are natural extensions from the previous recent ones, [7][8][9]11 where the authors have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method which is sub-supersolution. Here, in addition to the latter method, we use two other known methods, a direct variational method and Galerkin approach for proving some existence results to a logarithmic nonlinear elliptic equation of Kirchhoff-type with changing sign data.…”

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

“…Lemma 1 (see [14]). Under assumption (H1),we suppose further that function H(t) : � tM(t 2 ) is increasing on R.…”

“…Within previous studies [13][14][15], some nonlocal elliptical problems of the Kirchhoff type of the following model were extensively studied:…”

“…where Ω is a bounded open domain of R n with a smooth boundary zΩ and h(x, u) the right hand side is defined for some exceptional functions similar to those in [13][14][15][16]. In addition, M is a defined and continuous function on R + with values in R * + .…”

“…Motivated by the recent work in [13,14,18,19] and by using the sub-and supersolution method which is defined in [20], existence of positive solutions of quasi-linear Kirchhoff elliptic systems is shown in bounded smooth domains. e paper outline is as follows: some assumptions and definitions related to problem (1) are given in Section 2.…”