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Existence of Periodic Solutions of Semilinear Parabolic Equations and the Method of Upper and Lower Solutions

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Existence of Periodic Solutions of Semilinear Parabolic Equations and the Method of Upper and Lower Solutions

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dc.contributor.author Lakshmikantham, V. en
dc.contributor.author Kannan, R. en
dc.date.accessioned 2010-06-02T13:28:43Z en
dc.date.available 2010-06-02T13:28:43Z en
dc.date.issued 1982-04 en
dc.identifier.uri http://hdl.handle.net/10106/2227 en
dc.description.abstract The existence of periodic solutions of semilinear parabolic equations has been investigated by several authors [1-10,15-18] by different methods such as the method of Poincare operator and the theory of monotone operators. In a recent paper [1] Amann also obtains multiplicity results. Recently, an attempt was made successfully in [11,12,16] to combine the two basic techniques, namely the method of upper and lower solutions and the method of Lyapunov-Schmidt to investigate existence of periodic solutions of first and second order equations. In this paper we continue this fruitful approach to study existence of periodic solutions of semilinear parabolic equations with homogeneous Neumann boundary conditions. The results obtained are exhaustive in the sense that they not only contain the known results, but also deal with other possible situations. Although our approach is extendable to general case, we have considered a simple parabolic equation in one space variable so as to bring out the ideas involved clearly. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;179 en
dc.subject Parabolic equations en
dc.subject Periodic solutions en
dc.subject Semilinear parabolic equations en
dc.subject.lcsh Mathematics Research en
dc.title Existence of Periodic Solutions of Semilinear Parabolic Equations and the Method of Upper and Lower Solutions en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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