Difficulties in obtaining finite time blowup for fourth-order semilinear Schrödinger equations in the variational method frame

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dc.contributor.authorXu, Runzhang
dc.contributor.authorLin, Qiang
dc.contributor.authorChen, Shaohua
dc.contributor.authorWen, Guojun
dc.contributor.authorLian, Wei
dc.date.accessioned2021-11-29T19:23:31Z
dc.date.available2021-11-29T19:23:31Z
dc.date.issued2019-06-24
dc.description.abstractThis article concerns the Cauchy problem for fourth-order semilinear Schrodinger equations. By constructing a variational problem and some invariant manifolds, we prove the existence of a global solution. Then we analyze the difficulties in proving the finite time blowup of the solution for the corresponding problem in the frame of the variational method. Understanding the finite time blowup of solutions, without radial initial data, still remains an open problem.
dc.description.departmentMathematics
dc.formatText
dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationXu, R., Lin, Q., Chen, S., Wen, G., & Lian, W. (2019). Difficulties in obtaining finite time blowup for fourth-order semilinear Schrödinger equations in the variational method frame. <i>Electronic Journal of Differential Equations, 2019</i>(83), pp. 1-22.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14971
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFourth-order Schrödinger equation
dc.subjectGlobal solution
dc.subjectBlowup
dc.subjectVariational problem
dc.subjectInvariant manifolds
dc.titleDifficulties in obtaining finite time blowup for fourth-order semilinear Schrödinger equations in the variational method frame
dc.typeArticle

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