scholarly journals Solutions of 2nth-Order Boundary Value Problem for Difference Equation via Variational Method

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Qingrong Zou ◽  
Peixuan Weng
Keyword(s):  
Difference Equation ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Boundary Value

scholarly journals Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hongsen Fan ◽  
Zhiying Deng
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Exponent ◽  
Positive Solution ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity

AbstractIn this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.

scholarly journals Variational method for solving the boundary value problem of hydrodynamics

2021 ◽  
Vol 1047 (1) ◽  
pp. 012195
Author(s):  
D V Sysoev ◽  
A A Sysoeva ◽  
S A Sazonova ◽  
A V Zvyagintseva ◽  
N V Mozgovoj
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Boundary Value

Nonlinear Iterated Difference Inequalities

2012 ◽  
Vol 226-228 ◽  
pp. 2231-2234
Author(s):  
Wu Sheng Wang ◽  
Lian Juan Zhao
Keyword(s):  
Economic Development ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Natural Science ◽  
Social Economic ◽  
Boundary Value ◽  
Engineering Technology ◽  
Inequality Technique ◽  
Explicit Bounds ◽  
Social Economic Development

Motivated by Pachpatte difference inequalities and Abdeldaim integral inequalities, this paper establishes two generalized iterated difference inequalities, which consist of multiple iterated sums and contain both linear terms and nonlinear terms inside the sums. We obtain two new results which provide explicit bounds on unknown functions by difference inequality technique. The inequalities given here can be used as tools in the study of boundedness, uniqueness, stability and boundary value problem of a difference equation, which are important tools in studying of natural science, engineering technology, and the laws of social economic development.

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