Multiple solutions of nonlinear fractional elliptic equations via Morse theory

Multiple solutions of nonlinear fractional elliptic equations via Morse theory

This article concerns the existence and multiplicity of weak solutions of the nonlinear fractional elliptic problem. We extend some well known results of semilinear Laplacian equations to the nonlocal fractional setting. Using the variational methods based on the critical point theory, sub-supe...

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Bibliographic Details
Main Authors: Wei Qi, Lin Zhao, Xingjie Yan
Format: Article
Language:English
Published: Texas State University 2017-09-01
Series:Electronic Journal of Differential Equations
Subjects:
Fractional elliptic equation
critical point
Morse theory
critical group
sub-supersolutions
Online Access:http://ejde.math.txstate.edu/Volumes/2017/220/abstr.html
Description
Summary:This article concerns the existence and multiplicity of weak solutions of the nonlinear fractional elliptic problem. We extend some well known results of semilinear Laplacian equations to the nonlocal fractional setting. Using the variational methods based on the critical point theory, sub-supersolutions methods and Morse theory, we show that the problem has at least 6 nontrivial solutions.
ISSN:1072-6691

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