Asymptotics of the eigenvalues of self-adjoint fourth order differential operators with separated eigenvalue parameter dependent boundary conditions

2017 ◽  
Vol 47 (6) ◽  
pp. 2013-2042
Author(s):  
Manfred Möller ◽  
Bertin Zinsou
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Differential Operators ◽  
Eigenvalue Parameter ◽  
Parameter Dependent ◽  
Asymptotics Of The Eigenvalues

scholarly journals Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Manfred Möller ◽  
Bertin Zinsou
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Imaginary Axis ◽  
Order Ordinary Differential Equation ◽  
Eigenvalue Parameter ◽  
Upper Half Plane ◽  
Parameter Dependent ◽  
Asymptotics Of The Eigenvalues

Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameterλand which has separable boundary conditions depending linearly onλ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided.

Sign in / Sign up

Export Citation Format

Share Document