Kovalevskaya's theorem

Kovalevskaya's theorem states that certain complex differential equations, known as partial differential equations, have solutions that are well-behaved near specific points if those equations satisfy particular mathematical conditions. Essentially, it guarantees that under these conditions, the equations can be locally solved with power series expansions, providing predictable and stable solutions. This theorem helps mathematicians understand when complex systems modeled by such equations will have reliable solutions near initial points, ensuring the equations are mathematically consistent and useful for scientific and engineering problems.