On Eigenfunctions of the Boundary Value Problems for Second Order Differential Equations with Involution
Abstract
:1. Introduction
2. Green’s Function of the Operator
- (1)
- is continuous on the rectangle ;
- (2)
- The function has the continuous derivative for and satisfies the conditions:
- (3)
- The function has the derivative , satisfies (except at ) and (5).
- (1)
- is symmetric: , for all ;
- (2)
- is continuous on the rectangle ;
- (3)
- The function has the continuous derivative for , and satisfies the conditions:
- (4)
- The function has the derivative , satisfies except at ) and (4).
3. Green’s Function of the Operator
4. Basis Property of Eigenfunctons
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Sarsenbi, A.; Sarsenbi, A. On Eigenfunctions of the Boundary Value Problems for Second Order Differential Equations with Involution. Symmetry 2021, 13, 1972. https://doi.org/10.3390/sym13101972
Sarsenbi A, Sarsenbi A. On Eigenfunctions of the Boundary Value Problems for Second Order Differential Equations with Involution. Symmetry. 2021; 13(10):1972. https://doi.org/10.3390/sym13101972
Chicago/Turabian StyleSarsenbi, Abdissalam, and Abdizhahan Sarsenbi. 2021. "On Eigenfunctions of the Boundary Value Problems for Second Order Differential Equations with Involution" Symmetry 13, no. 10: 1972. https://doi.org/10.3390/sym13101972
APA StyleSarsenbi, A., & Sarsenbi, A. (2021). On Eigenfunctions of the Boundary Value Problems for Second Order Differential Equations with Involution. Symmetry, 13(10), 1972. https://doi.org/10.3390/sym13101972