Generalization of sturm-picone theorem for second-order nonlinear differential equations

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dc.contributor.author Tyagi, Jagmohan
dc.date.accessioned 2014-03-18T17:13:15Z
dc.date.available 2014-03-18T17:13:15Z
dc.date.issued 2013-01
dc.identifier.citation Tyagi, Jagmohan, “Generalization of sturm-picone theorem for second-order nonlinear differential equations”, Taiwanese Journal of Mathematics, DOI: 10.11650/tjm.17.2013.2074, vol.17, no. 1, pp. 361-378, Jan. 2013. en_US
dc.identifier.issn 2224-6851
dc.identifier.issn 1027-5487
dc.identifier.uri http://dx.doi.org/10.11650/tjm.17.2013.2074
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/906
dc.description.abstract The goal of this paper is to show a generalization to Sturm--Picone theorem for a pair of second-order nonlinear differential equations (p_1(t)x'(t))'+ q_1(t)f_{1}(x(t))=0. (p_2(t)y'(t))'+ q_2(t)f_{2}(y(t))=0, ,t_1<t<t_2. This work generalizes well-known comparison theorems [C. Sturm, J. Math.Pures. Appl. 1 (1836), 106--186; M. Picone, Ann. Scoula\,Norm.\,Sup.\,Pisa, 11 (1909),39; W. Leighton, Proc. Amer. Math. Soc.13 (1962), 603--610], which play a key role in the qualitative behavior of solutions. We establish the generalization to a pair of nonlinear singular differential equations and elliptic partial differential equations also. We show generalization via the quadratic functionals associated to the above pair of equations. The celebrated Sturm--Picone theorem for a pair of linear differential equations turns out to be a particular case of our result. We also use these comparison theorems to ensure the oscillatory as well as nonoscillatory behavior of solutions for a class of nonlinear equations. en_US
dc.description.statementofresponsibility by Jagmohan Tyagi
dc.format.extent Vol.17, No. 1, pp. 361-378
dc.language.iso en en_US
dc.publisher The Mathematical Society of the Republic China en_US
dc.subject Elliptic partial differential equations en_US
dc.subject Oscillatory as well as nonoscillatory behavior en_US
dc.subject Singular equation en_US
dc.title Generalization of sturm-picone theorem for second-order nonlinear differential equations en_US
dc.type Article en_US
dc.relation.journal Taiwanese Journal of Mathematics


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