A necessary and sufficient condition for existence of positive solutions of nonlinear boundary value problems

2007 ◽  
Vol 66 (11) ◽  
pp. 2389-2412 ◽  
Author(s):  
John R. Graef ◽  
Lingju Kong
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Nonlinear Boundary Value Problems ◽  
Existence Of Positive Solutions ◽  
Nonlinear Boundary Value ◽  
Necessary And Sufficient

scholarly journals Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Baoqiang Yan ◽  
Meng Zhang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient ◽  
Monge Ampere

This paper considers the following boundary value problem:((-u'(t))n)'=ntn-1f(u(t)),  0<t<1,  u'(0)=0,  u(1)=0, wheren>1is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions.

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