On Bounded Positive Solutions For A Third Order Nonlinear Neutral Differential Equation

This paper is mainly concerned with the existence and multiplicity of third order nonlinear neutral differential equation where k∈N and t0∈R are constants, a,b,c,τ,gj∈C([t0,+∞),R), a([t0,+∞))(?)R\{0}, With respect to several ranges of function b, by using the Leray-Schauder nonlinear alternative theorem, Rothe fixed point theorem, Krasnoselskill fixed point theorem, Schauder fixed point theorem and some new techniques, we prove the existence of uncountably many bounded positive solutions for the above equation under certain conditions. The results presented in this paper extend and improve genuinely all results in [9]. Finally five nontrivial examples are presented to apply Theorems3.1-3.5.