Definition of a Differential Eigenvalue Problem?

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Homework Help Overview

The discussion revolves around the definition of a Differential Eigenvalue Problem, specifically focusing on the relationship between linear operators and eigenvalues in the context of differential equations.

Discussion Character

  • Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand the definition of a Differential Eigenvalue Problem and has provided a basic equation involving eigenvalues and linear operators. Some participants clarify the concepts of eigenfunctions and eigenvalues, while others question the specific use of the term "differential."

Discussion Status

The discussion is ongoing, with some participants providing clarifications on the definitions involved. There is a noted inquiry into the term "differential," indicating that further exploration of this aspect may be necessary.

Contextual Notes

The original poster is a mathematics undergraduate, which may influence the level of detail and complexity in the explanations sought.

dev00790
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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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