Definition of a Differential Eigenvalue Problem?

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A Differential Eigenvalue Problem involves a linear operator acting on a function, resulting in a constant multiple of that function, known as an eigenfunction, with the corresponding constant being the eigenvalue. The equation typically used is λy = Ly, where λ represents the eigenvalue and L is the linear operator. The term "differential" refers to operators that involve derivatives, commonly seen in differential equations. Understanding this concept is crucial for solving various mathematical and physical problems. Clarifying the role of differential operators can enhance comprehension of the overall topic.
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Homework Statement



I would like to know what the definition of a Differential Eigenvalue Problem is please?
I am a maths undergraduate.

Homework Equations



\lambda y = L y, where \lambda is eigenvalue, L is a linear operator.

The Attempt at a Solution



I have searched via google, encylopedia britanica, wikipedia but only have a vague understanding. If someone could help me define it that would be great.

Thank you. :smile:
 
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You just defined it. If an operator acts on a function and returns a constant multiple of that function then the function is an 'eigenfunction' and the value of the multiple is 'eigenvalue'. That's really all there is to it.
 
Thanks a lot :).
 
But why "differential"? :redface:
 

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