Global Existence Of Nonoscillatory Solutions For A Third Order Nonlinear Neutral Delay Differential Equation And Their Applications

This paper is concerned with the global existence of nonoscillatory solutions for the third order nonlinear neutral delay differential equation Some sufficient conditions for the existence of uncountably many bounded nonoscillatory solutions are presented for the above differential equation by virtue of the Krasnoselskii's fixed point theorem and Schauder's fixed point theorem. Our results presented in this paper extend, sharp and improve Theorem in [3], Theorems 2.2-2.10 in [6], Theorems A and B in [9], Theorems 1-3 in [10], Theorem 1 in [11], Theorems 1-3 in [13], Theorems 1-3 in [16], Theorem in [17], Theorems 1 and 2 in [18], and Theorems 1 and 2 in [19]. Seven examples are constructed to demonstrate the importance and the applications of the theorems obtained in this paper.