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Are there differential equations that, for some reason, don't have a Green function? Are there conditions for a DE to satisfy so that it can have a Green function?
Thanks
Thanks
But can be used for all linear DEs?pasmith said:The entire concept is useless for non-linear DEs.
pasmith said:The entire concept is useless for non-linear DEs.
Differential equations without Green functions are equations that describe the relationship between an unknown function and its derivatives. Unlike Green functions, which are used to solve boundary value problems, these equations do not require a specific boundary condition to be solved.
These equations can be solved using various methods such as separation of variables, substitution, and series expansion. The exact method used depends on the specific equation and its characteristics.
These equations have a wide range of applications in fields such as physics, engineering, and economics. They are commonly used to model physical systems and phenomena, and to make predictions and analyze data.
The main difference is that differential equations without Green functions do not require specific boundary conditions to be solved, whereas differential equations with Green functions do. This makes them more versatile and applicable to a wider range of problems.
While they offer more flexibility, these equations can be more difficult to solve compared to those with Green functions. Additionally, they may not provide as much insight into the underlying dynamics of a system, as the presence of Green functions allows for a more intuitive understanding of the solution.