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Positive periodic solutions and eigenvalue intervals for systems of second order differential equations
Author(s) -
Chu Jifeng,
Chen Hao,
O'Regan Donal
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510695
Subject(s) - mathematics , eigenvalues and eigenvectors , order (exchange) , fixed point theorem , cone (formal languages) , differential equation , mathematical analysis , comparison theorem , interval (graph theory) , fixed point , pure mathematics , combinatorics , physics , quantum mechanics , algorithm , finance , economics
In this paper, we employ a well‐known fixed point theorem for cones to study the existence of positive periodic solutions to the n ‐dimensional system x ″ + A ( t ) x = H ( t ) G ( x ). Moreover, the eigenvalue intervals for x ″ + A ( t ) x = λH ( t ) G ( x ) are easily characterized. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)