Title:	Travelling wave solutions of the beam equation with jumping nonlinearity
Authors:	Holubová, Gabriela Levá, Hana
Citation:	HOLUBOVÁ, G. LEVÁ, H. Travelling wave solutions of the beam equation with jumping nonlinearity. Journal of Mathematical Analysis and Applications, 2023, roč. 527, č. 2, s. 1-15. ISSN: 0022-247X
Issue Date:	2023
Publisher:	Academic Press
Document type:	článek article
URI:	2-s2.0-85161632949 http://hdl.handle.net/11025/54562
ISSN:	0022-247X
Keywords in different language:	travelling wave;beam equation;jumping nonlinearity;mountain pass theorem
Abstract in different language:	We study the existence of travelling wave solutions of a nonlinear fourth–order partial differential equation which can be considered as a model of an asymmetrically supported beam. We use a variational approach and show that there exist infinitely many travelling wave solutions under considerably weakened assumptions than those previously used in the literature. On the other hand, allowing the presence of sign preserving nonlinearities results in a limitation of the possible values of the wave speed. We pose several questions that still remain open, particularly regarding the range of wave speeds and the number of solutions. Moreover, some forms of classical solutions are presented together with some numerical experiments.
Rights:	Plný text je přístupný v rámci univerzity přihlášeným uživatelům © Elsevier
Appears in Collections:	Články / Articles (NTIS) Články / Articles (KMA) OBD

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