Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Multiplicity and regularity of large periodic solutions with rational frequency for a class of semilinear monotone wave equations


Author: Jean-Marcel Fokam
Journal: Proc. Amer. Math. Soc. 145 (2017), 4283-4297
MSC (2010): Primary 35B45, 35B10, 42B35, 49J35, 35J20, 35L10, 35L05
DOI: https://doi.org/10.1090/proc/12760
Published electronically: July 10, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence of infinitely many classical large periodic solutions for a class of semilinear wave equations with periodic boundary conditions:

$\displaystyle u_{tt}-u_{xx}+f(x,u)=0, $

$\displaystyle u(0,t)=u(\pi ,t)\,\,\,, u_x(0,t)=u_x(\pi ,t). $

Our argument relies on some new estimates for the linear problem with periodic boundary conditions, the Hausdorff-Young theorem of harmonic analysis and a variational formulation due to Rabinowitz. We also develop a new approach to the regularity of the distributional solutions by differentiating the equations and employing Gagliardo-Nirenberg estimates.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35B45, 35B10, 42B35, 49J35, 35J20, 35L10, 35L05

Retrieve articles in all journals with MSC (2010): 35B45, 35B10, 42B35, 49J35, 35J20, 35L10, 35L05


Additional Information

Jean-Marcel Fokam
Affiliation: School of Arts and Sciences, American University of Nigeria, Yola, Nigeria
Email: fokam@aun.edu.ng

DOI: https://doi.org/10.1090/proc/12760
Received by editor(s): February 12, 2012
Received by editor(s) in revised form: September 13, 2013, September 3, 2014, and February 16, 2015
Published electronically: July 10, 2017
Communicated by: Walter Craig
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society