scholarly journals Boundary value problems for second-order differential operator equations

1986 ◽  
Vol 83 ◽  
pp. 29-38 ◽  
Author(s):  
Lucas Jódar
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Order Differential Operator ◽  
Operator Equations

Stability of Solutions of Differential-operator and Operator-difference Equations in the Sense of Perturbation of Operators

2006 ◽  
Vol 6 (3) ◽  
pp. 269-290 ◽  
Author(s):  
B. S. Jovanović ◽  
S. V. Lemeshevsky ◽  
P. P. Matus ◽  
P. N. Vabishchevich
Keyword(s):  
Differential Operator ◽  
Difference Equations ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Order Differential Operator ◽  
Stability Of Solutions ◽  
Operator Equations ◽  
The Difference ◽  
Coefficient Stability

Abstract Estimates of stability in the sense perturbation of the operator for solving first- and second-order differential-operator equations have been obtained. For two- and three-level operator-difference schemes with weights similar estimates hold. Using the results obtained, we construct estimates of the coefficient stability for onedimensional parabolic and hyperbolic equations as well as for the difference schemes approximating the corresponding differential problems.

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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