Positive solutions to singular system with four-point coupled boundary conditions

Multiplicity Results for Positive Solutions to Differential Systems of Singular Coupled Integral Boundary Value Problems

“…Naturally we hope there are the same excellent results on singular uncoupled boundary value problems to differential systems with coupled boundary conditions. Many researchers put their efforts to study the existence of solutions for differential systems with coupled boundary conditions (see [19][20][21][22][23][24][25][26][27][28][29][30] and references therein).…”

“…In [19], Asif and Khan addressed the question of the existence of coupled four-point boundary value conditions − ( ) = 1 ( , ( ) , ( )) , ∈ (0, 1) , − ( ) = 2 ( , ( ) , ( )) , ∈ (0, 1) , (0) = (0) = 0,…”

“…We should note that the nonlinear terms in two equations for the above problems have the same features. For instance, the nonlinear terms in two equations are both superlinear [20,29] or both sublinear [19]. However, to the best of our knowledge, only a few papers discuss differential system under the case that the nonlinear terms of the system have different behaviors.…”

“…However, to the best of our knowledge, only a few papers discuss differential system under the case that the nonlinear terms of the system have different behaviors. Motivated by [19,20,29], the purpose of this paper is to establish the existence of multiple positive solutions for differential system with coupled integral boundary value problems (3) when 1 is superlinear in and and 2 is sublinear in and . Also suppose that 1 ( , , ) may be singular at = 0, = 1 and 2 ( , , ) may be singular at = 0, = 1, = 0, and = 0.…”

Non-negative solutions of systems of ODEs with coupled boundary conditions

“…Systems with coupled BCs can be applied to Lotka-Volterra models, reaction-diffusion phenomena and interaction problems, see for example the works of Amann [7], Leung [24] and Mehmeti and Nicaise [27]. A recent paper in this line of research is the one by Asif and Khan [8], who study the four-point coupled system u 00 ðtÞ þ f 1 ðt; uðtÞ; vðtÞÞ ¼ 0; t 2 ð0; 1Þ; v 00 ðtÞ þ f 2 ðt; uðtÞ; vðtÞÞ ¼ 0; t 2 ð0; 1Þ; uð0Þ ¼ 0; uð1Þ ¼ d 12 …”