Periodic solutions of systems with asymptotically even nonlinearities. (2000)

• Record Type: Journal Article
• Authors: Kloeden, Peter E.; Krasnosel'skii, Alexander M.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 1(2000)
• Page Start: 41
• Page End: 50
• Publication Date: 2000
• Subjects: index at infinity -- degenerate linear part -- asymptotically even nonlinearity -- boundary value problems; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000058
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate “next order” terms are obtained for the 2 π -periodic problem for the scalar equation x ″ + n 2 x = g ( | x | ) + f ( t, x ) + b ( t ) with bounded g ( u ) and f ( t, x ) → 0 as | x | → 0 . The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory.