Existence results of periodic solutions for third‐order nonlinear singular differential equation

Abstract

Using Green's function for third‐order differential equation and some fixed‐point theorems, i.e., Leray‐Schauder alternative principle and Schauder's fixed point theorem, we establish three new existence results of periodic solutions for nonlinear third‐order singular differential equation, which extend and improve significantly existing results in the literature.

Multiplicity results of positive solutions for fourth‐order nonlinear differential equation with singularity

“…Next, we will consider G 2i .t, s/, which can be found in [12]. The associated homogeneous equation of (2.3) is…”

“…Taliaferro's work has attracted the attention of many specialists in differential equations. More recently, the method of lower and upper solutions, the Poincaré-Birkhoff twist theorem, the Schauder's fixed-point theorem, and the Krasnoselskii fixed-point theorem in a cone have been employed to investigate the existence of positive periodic solutions of singular differential equations (e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

Multiplicity Results for Variable-Coefficient Singular Third-Order Differential Equation with a Parameter

“…At the beginning, most of work concentrated on secondorder singular differential equations, as in the references we mentioned above. Recently, there have been published some results on third-order singular differential equation (see [14][15][16][17][18][19]). For example, in [14], Chu and Zhou considered the following third-order singular differential equation:…”

Existence of positive periodic solution for variable-coefficient third-order differential equation with singularity

“…Third‐order differential equations arise in a variety of areas in agriculture, biology, economics, and physics and attract much attention, see and the references cited therein. For example, in , Chu and Zhou considered a third‐order singular differential equation with periodic boundary conditions u ( i ) (0) = u ( i ) (2 π ), i = 0,1,2.…”

“…Third-order differential equations arise in a variety of areas in agriculture, biology, economics, and physics [1][2][3][4][5] and attract much attention, see [6][7][8][9][10][11][12][13][14][15] and the references cited therein. For example, in [10], Chu and Zhou considered a third-order singular differential equation…”