Question: I am trying to solve a set of ODEs with dsolve, but when the parameter value(lambda) is larger then 0.11 the dsolve fails to solve. Anyone could give me some guidance?

I am trying to solve a set of ODEs with dsolve. There are 26 equations of my ODEs, but the problem is a multiple point bvp. So the range is divided into three region. In order to use dsolve, I transform the three subregion's coordinate into 0 to 1. Meanwhile, the ODEs are different in three regions, respectively. So, there are 26×3 equations in total. And according to the paper I want to replicate, it says the response is unstable,so parameter continuation is used. Similar to the paper, an additional equation is added(eq1_27 in code), also an additional condition is added(about lambda). When the lambda is less then 0.11, the dsolve works, but for other values it doesn't work. Could anyone help me?

Sorry for the tedious programming code, I am new to Maple.