Positive solutions of a system of second order boundary value problems involving first order derivatives via -monotone matrices

Semilinear Elliptic Systems with Dependence on the Gradient

“…Radial solutions of elliptic systems have been studied with topological methods in [5,6,7,8,18,19,20], in particular the cones have been used in [6,18,19]. The use of cones and Harnack-type inequalities in the context of ordinary differential equations or systems depending on the first derivative has been studied in [1,3,7,12,14,15,21,22]. The paper is organized as follows: in Section 2 we introduce and prove our auxiliary results, in particular the properties of a suitable compact operator, Section 3 contains the existence and non-existence results for the elliptic sistem and an example.…”

Existence and Multiplicity of Positive Solutions for a System of Fourth-Order Boundary Value Problems

“…Consequently, fourth-order boundary value problems play a very important role in both theory and applications. Boundary value problems for systems of nonlinear ordinary differential equations have been also studied by several authors; for example, see [3][4][5][6][7][8][9][10][11] and the references therein. In [3], Li…”

“…where , ∈ ([0, 1] × R + , R + ). In [11], the authors investigate the existence and multiplicity of positive solutions for the system (−1) (2 ) = ( , , , − , . .…”

Positive Solutions for a System of Fourth-Order p-Laplacian Boundary Value Problems

“…Based on a priori estimates achieved by utilizing the Jensen integral inequalities and R + -monotone matrices, the author used fixed point index theory to establish the existence and multiplicity of positive solutions for the previous problem. For more details of the recent progress in the boundary value problems for systems of nonlinear ordinary differential equations, we refer the reader to [19][20][21][22][23][24][25][26][27] and the references cited therein.…”