Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces

2009 ◽  
Vol 79 (1) ◽  
pp. 22-54 ◽  
Author(s):  
Angelo Favini ◽  
Veli Shakhmurov ◽  
Yakov Yakubov
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Boundary Value ◽  
Second Order ◽  
Elliptic Differential Operator ◽  
Regular Boundary ◽  
Operator Equations ◽  
Umd Banach Spaces

scholarly journals Nonlinear Sum Operator Equations with a Parameter and Application to Second-Order Three-Point BVPs

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wen-Xia Wang ◽  
Xi-Lan Liu ◽  
Piao-Piao Shi
Keyword(s):  
Nonlinear Analysis ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Critical Value ◽  
Second Order ◽  
Point Boundary ◽  
Operator Equations

A class of nonlinear sum operator equations with a parameter on order Banach spaces were considered. The existence and uniqueness of positive solutions for this kind of operator equations and the dependence of solutions on the parameter have been obtained by using the properties of cone and nonlinear analysis methods. The critical value of the parameter was estimated. Further, the application to some nonlinear three-point boundary value problems was given to show the significance of the discussion.

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