A second-order adaptive grid method for a nonlinear singularly perturbed problem with an integral boundary condition

2021 ◽  
Vol 385 ◽  
pp. 113205 ◽  
Author(s):  
Zhongdi Cen ◽  
Li-Bin Liu ◽  
Aimin Xu
Keyword(s):  
Boundary Condition ◽  
Grid Method ◽  
Adaptive Grid ◽  
Second Order ◽  
Singularly Perturbed ◽  
Integral Boundary Condition ◽  
Singularly Perturbed Problem ◽  
Integral Boundary

scholarly journals Existence of Multiple Solutions for Second-Order Problem with Stieltjes Integral Boundary Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Qing-Qing Hu ◽  
Baoqiang Yan
Keyword(s):  
Boundary Condition ◽  
Variational Method ◽  
Multiple Solutions ◽  
Order Equation ◽  
Second Order ◽  
Integral Boundary Condition ◽  
Stieltjes Integral ◽  
Order Problem ◽  
Integral Boundary ◽  
Critical Point Theorem

In this paper, we consider the existence of multiple solutions for second-order equation with Stieltjes integral boundary condition using the three-critical-point theorem and variational method. Firstly, a novel space is established and proved to be Hilbert one. Secondly, based on the above work, we obtain the existence of multiple solutions for our problem. Finally, in order to illustrate the effectiveness of our problem better, the example is listed.

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