A solution to a fractional order semilinear equation using variational method
We will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Western Libraries
2020-11-01
|
Series: | Mathematics in Applied Sciences and Engineering |
Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/9413 |
id |
doaj-a895714b6dad4a56891cf7e0b58ab7bb |
---|---|
record_format |
Article |
spelling |
doaj-a895714b6dad4a56891cf7e0b58ab7bb2021-08-05T21:45:54ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262020-11-011427528510.5206/mase/94133728A solution to a fractional order semilinear equation using variational methodRamesh Karki0Young Hwan YouIndiana University EastWe will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional whose Euler-Lagrange equation is the given semilinear pseudo-differential equation, and also discuss the regularity of such a minimizer so that it will be a solution to the semilinear equation.https://ojs.lib.uwo.ca/index.php/mase/article/view/9413 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ramesh Karki Young Hwan You |
spellingShingle |
Ramesh Karki Young Hwan You A solution to a fractional order semilinear equation using variational method Mathematics in Applied Sciences and Engineering |
author_facet |
Ramesh Karki Young Hwan You |
author_sort |
Ramesh Karki |
title |
A solution to a fractional order semilinear equation using variational method |
title_short |
A solution to a fractional order semilinear equation using variational method |
title_full |
A solution to a fractional order semilinear equation using variational method |
title_fullStr |
A solution to a fractional order semilinear equation using variational method |
title_full_unstemmed |
A solution to a fractional order semilinear equation using variational method |
title_sort |
solution to a fractional order semilinear equation using variational method |
publisher |
Western Libraries |
series |
Mathematics in Applied Sciences and Engineering |
issn |
2563-1926 |
publishDate |
2020-11-01 |
description |
We will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional whose Euler-Lagrange equation is the given semilinear pseudo-differential equation, and also discuss the regularity of such a minimizer so that it will be a solution to the semilinear equation. |
url |
https://ojs.lib.uwo.ca/index.php/mase/article/view/9413 |
work_keys_str_mv |
AT rameshkarki asolutiontoafractionalordersemilinearequationusingvariationalmethod AT younghwanyou asolutiontoafractionalordersemilinearequationusingvariationalmethod AT rameshkarki solutiontoafractionalordersemilinearequationusingvariationalmethod AT younghwanyou solutiontoafractionalordersemilinearequationusingvariationalmethod |
_version_ |
1721219899560296448 |