##  [Lyapunov–Schmidt Reduction](/lyapunov-schmidt-reduction) 

  ##  [Lyapunov–Schmidt Reduction](https://puremath.quantumdictionary.io/lyapunov-schmidt-reduction-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A finite-dimensional reduction technique that splits an operator equation F(u)=0 in a Banach space into range and kernel components via projections, solves the range equation for the complement, and reduces solvability and bifurcation analysis to a finite-dimensional problem on the kernel.