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...

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Main Authors: Ramesh Karki, Young Hwan You
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
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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
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AT younghwanyou asolutiontoafractionalordersemilinearequationusingvariationalmethod
AT rameshkarki solutiontoafractionalordersemilinearequationusingvariationalmethod
AT younghwanyou solutiontoafractionalordersemilinearequationusingvariationalmethod
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