Abstract
This work is devoted to the study of multiplicity results of solutions for a class of nonlinear equations involving the square root of the Laplacian. Indeed, we will use variational methods for smooth functionals, defined on reflexive Banach spaces, in order to achieve the existence of at least three solutions for the equations. Moreover, assuming that the nonlinear terms are nonnegative, we will prove that the solutions are nonnegative. Finally, by presenting an example, we will ensure the applicability of our results.
Recommended Citation
M. Bohner et al., "Critical Point Approaches to Nonlinear Square Root Laplacian Equations," Miskolc Mathematical Notes, vol. 25, no. 1, pp. 153 - 164, Miskolc Mathematical Notes, Jan 2024.
The definitive version is available at https://doi.org/10.18514/MMN.2024.4258
Department(s)
Mathematics and Statistics
Keywords and Phrases
fractional Laplacian; infinitely many solutions; one solution; variational methods; weak solutions
International Standard Serial Number (ISSN)
1787-2413; 1787-2405
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Miskolc Mathematical Notes, All rights reserved.
Publication Date
01 Jan 2024
