A weak extension theorem for inhomogeneous differential equations

2001 ◽  
Vol 13 (3) ◽  
Author(s):  
Mitsuru Sugimoto
Keyword(s):  
Differential Equations ◽  
Extension Theorem ◽  
Weak Extension

scholarly journals Building Infinitely Many Solutions for Some Model of Sublinear Multipoint Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Guy Aymard Degla
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Extension Theorem ◽  
Existence Results ◽  
Infinitely Many Solutions ◽  
Qualitative Result ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

We show that the sublinearity hypothesis of some well-known existence results on multipoint Boundary Value Problems (in short BVPs) may allow the existence of infinitely many solutions by using Tietze extension theorem. This is a qualitative result which is of concern in Applied Analysis and can motivate more research on the conditions that ascertain the existence of multiple solutions to sublinear BVPs. The idea of the proof is of independent interest since it shows a constructive way to have ordinary differential equations with multiple solutions.

scholarly journals Application and simplified proof of a sharp L2 extension theorem

2015 ◽  
Vol 220 ◽  
pp. 81-89 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bergman Kernel ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Stability Theorem ◽  
Alternate Proof

AbstractAs an application of a sharp L2 extension theorem for holomorphic functions in Guan and Zhou, a stability theorem for the boundary asymptotics of the Bergman kernel is proved. An alternate proof of the extension theorem is given, too. It is a simplified proof in the sense that it is free from ordinary differential equations.

scholarly journals Application and simplified proof of a sharp L2 extension theorem

2015 ◽  
Vol 220 ◽  
pp. 81-89 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bergman Kernel ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Stability Theorem ◽  
Alternate Proof

AbstractAs an application of a sharpL2extension theorem for holomorphic functions in Guan and Zhou, a stability theorem for the boundary asymptotics of the Bergman kernel is proved. An alternate proof of the extension theorem is given, too. It is a simplified proof in the sense that it is free from ordinary differential equations.

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