Bounded Nonoscillatory Solutions For A Higher Order Nonlinear Neutral Delay Differential Equation

This paper aims to deal with the solvability of the higher order nonlinear neutral delay differential equation whereτ>0,n∈N\{1},m,k,l∈N, r,p,h,qi,αi,βj,γc∈C([t0,+∞),R),f∈C([t0,+∞)×Rk,R) and g∈C([t0,+∞)×R1,R)satisfying(?)=+∞, i∈{1,2,…m},j∈{1,2,…k},c∈{1,2,…l). With respect to various ranges of function p, we investigate some sufficient conditions for the existence of uncountably many bounded nonoscillatory solutions for the above equation. The main tools used in this paper are the Krasnoselskii's and Schauder's fixed point theorems. Our results presented in this paper extend, improve and unify Theorem in [14], Theorem in [5], Theorem 2.1 in [12], Theorems 2 and 3 in [19], Theorems 1-3 in [2], Theorems 2.1 and 2.3 in [21], Theorems 1-4 and 6 in [11], Theorems 1-4 in [7].