Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Yucheng Bu
Pages: [61] - [75]
Received Date: March 17, 2017; Revised April 19, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121801
In this paper, a class of 2p-order ordinary differential equation with periodic nonlinearity are concerned. Several assumptions are made by an index theory for the corresponding linear homogeneous equation. Under these assumptions, a multiplicity result of solutions for the concerned equation is obtained by applying Lyapunov-Schmidt reduction and a careful analysis of the oscillatory behaviour of the bifurcation equation induced by the concerned equation.
ordinary differential equation, index theory, Lyapunov-Schmidt reduction, resonance, periodic nonlinearity.
