Asymptotics of Eigenvalues for Many-Particle Hamiltonians at Symmetry Subspaces

1990 ◽  
pp. 55-59
Author(s):  
S. A. Vugal’ter
Keyword(s):  
Asymptotics Of Eigenvalues

scholarly journals STURM–LIOUVILLE PROBLEMS WITH BOUNDARY CONDITIONS RATIONALLY DEPENDENT ON THE EIGENPARAMETER. I

2002 ◽  
Vol 45 (3) ◽  
pp. 631-645 ◽  
Author(s):  
Paul A. Binding ◽  
Patrick J. Browne ◽  
Bruce A. Watson
Keyword(s):  
Boundary Conditions ◽  
Liouville Equation ◽  
Subject Classification ◽  
Asymptotics Of Eigenvalues ◽  
Primary 34B24 ◽  
Sturm Liouville

AbstractWe consider the Sturm–Liouville equation$$ -y''+qy=\lambda y\quad\text{on }[0,1], $$subject to the boundary conditions$$ y(0)\cos\alpha=y'(0)\sin\alpha,\quad\alpha\in[0,\pi), $$and$$\frac{y'}{y}(1)=a\lambda+b-\sum_{k=1}^N\frac{b_k}{\lambda-c_k}. $$Topics treated include existence and asymptotics of eigenvalues, oscillation of eigenfunctions, and transformations between such problems.AMS 2000 Mathematics subject classification: Primary 34B24; 34L20

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