scholarly journals Blowup Analysis for a Semilinear Parabolic System with Nonlocal Boundary Condition

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Yulan Wang ◽  
Zhaoyin Xiang
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Semilinear Parabolic System ◽  
Semilinear Parabolic

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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