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dc.contributor.authorLin, Genghong ( )
dc.contributor.authorYu, Jianshe ( )
dc.contributor.authorZhou, Zhan ( )
dc.date.accessioned2021-12-01T20:44:19Z
dc.date.available2021-12-01T20:44:19Z
dc.date.issued2019-08-02
dc.identifier.citationLin, G., Yu, J., & Zhou, Z. (2019). Homoclinic solutions of discrete nonlinear Schrodinger equations with partially sublinear nonlinearities. Electronic Journal of Differential Equations, 2019(96), pp. 1-14.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14987
dc.description.abstractWe consider a class of discrete nonlinear Schrodinger (DNLS) equations in m dimensional lattices with partially sublinear nonlinearity f. Combining variational methods and a priori estimate, we give a general sufficient condition on f for type (A), that is, a sequence of nontrivial homoclinic solutions accumulating to zero. By using a compact embedding technique, we overcome the loss of compactness due to the problem being set on the unbounded domain ℤm. Another obstacle caused by the local definition of f is solved by using the cutoff methods to recover the global property of f. To the best of our knowledge, this is the first time to obtain infinitely many homoclinic solutions for the DNLS equations with partially sublinear nonlinearity. Moreover, we prove that if f is not sublinear, the zero solution is isolated from other homoclinic solutions. Our results show that the sublinearity and oddness of f yield type (A). Without the oddness assumption, we still can prove that this problem has at least a nontrivial homoclinic solution if f is local sublinear, which improves some existing results.en_US
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDiscrete nonlinear Schrödinger equationen_US
dc.subjectDiscrete breathersen_US
dc.subjectHomoclinic solutionen_US
dc.subjectPartially sublinear nonlinearitiesen_US
dc.subjectVariational methoden_US
dc.titleHomoclinic solutions of discrete nonlinear Schrodinger equations with partially sublinear nonlinearitiesen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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