Necessary and sufficient condition for the positivity of the Green function of a boundary value problem for a fourth-order equation on a graph

2015 ◽  
Vol 51 (3) ◽  
pp. 303-317 ◽  
Author(s):  
R. Ch. Kulaev
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Order Equation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Fourth Order Equation ◽  
The Green Function ◽  
Necessary And Sufficient

scholarly journals Existence of Positive Solutions for Some Superlinear Fourth-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Imed Bachar ◽  
Habib Mâagli
Keyword(s):  
Green Function ◽  
Fourth Order ◽  
Integrability Condition ◽  
Order Equation ◽  
Global Behavior ◽  
Fourth Order Equation ◽  
Existence Of Positive Solutions ◽  
Nonnegative Continuous Function ◽  
The Green Function ◽  
Perturbation Arguments

We are concerned with the following superlinear fourth-order equationu4t+utφt,−ut=0,   t∈0, 1;−u0=u1=0,  −u′0=a,  −u′1=-b, wherea,−bare nonnegative constants such thata+b>0andφt,−sis a nonnegative continuous function that is required to satisfy some appropriate conditions related to a classKsatisfying suitable integrability condition. Our purpose is to prove the existence, uniqueness, and global behavior of a classical positive solution to the above problem by using a method based on estimates on the Green function and perturbation arguments.

scholarly journals On Removable Sets of the First Boundary-Value Problem for Degenerated Elliptic Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-20
Author(s):  
Tair S. Gadjiev ◽  
Asghar I. Shariffar ◽  
Rafig A. Rasulov
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Removable Sets ◽  
Necessary And Sufficient

In the paper, the necessary and sufficient condition of compact removability is obtained.

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