Uncountable Many Bounded Positive Solutions For A Second Order Nonlinear Differential Equation With Forcing Term

The purpose of this paper is to deal with the second order nonlinear neutral delaydifferential equation with forcing termAccording to different ranges of the function c (t), the full text is divided into five parts,and by means of Krasnoselskii fixed point theorem and Schauder fixed point theorem to studythe existence of uncountable many bounded positive solutions. In each part, one or twomapings are constructed, and then the mapings are proved to satisfy the conditions of thefixed point theorems which are used in the part. Finally, according to the corresponding fixedpoint theorems, the conditions to ensure the existence of uncountable many bounded positivesolutions of the second order nonlinear neutral delay differential equation are obtained.The results presented in this paper extend and improve essentially the known results inthis field. In the end, five nontrivial examples are constructed as applications of our results.