%0 Journal Article %T A higher order nonlinear neutral differential equation %A Jiang, Guojing %A Sun, Wei %A An, Zhefu %A Zhao, Liangshi %J Journal of Nonlinear Sciences and Applications %D 2019 %V 12 %N 10 %@ ISSN 2008-1901 %F Jiang2019 %X This paper is concerned with the higher order nonlinear neutral differential equation \[ [a(t)(x(t)+b(t)x(\tau(t)))']^{(n-1)}+f(t, x(g_1(t)),\ldots, x(g_k(t)))=c(t),\quad t\ge t_0. \] By dint of the Leray-Schauder nonlinear alternative, Rothe fixed point theorem and some new techniques, we prove the existence of uncountably many bounded positive solutions for the equation. Several nontrivial examples are given to illustrate the applications and advantages of the results presented in this paper. %9 journal article %R 10.22436/jnsa.012.10.06 %U http://dx.doi.org/10.22436/jnsa.012.10.06 %P 675--698 %0 Journal Article %T Nonoscillatory solutions for discrete equations %A R. P. Agarwal %A S. R. Grace %A D. O'Regan %J Comput. Math. Appl. %D 2003 %V 45 %F Agarwal2003 %0 Book %T Nonlinear Functional Analysis %A K. Deimling %D 1985 %I Springer-Verlag %C Berlin %F Deimling1985 %0 Journal Article %T Existence and mann iterative approximations of nonoscillatory solutions of nth order neutral delay differential equations %A Z. Liu %A H. Gao %A S. M. Kang %A S. H. Shim %J J. Math. Anal. Appl. %D 2007 %V 329 %F Liu2007 %0 Journal Article %T Existence of positive solutions of second order nonlinear neutral differential equations with positive and negative terms %A Z. G. Zhang %A A. J. Yang %A C. N. Di %J J. Appl. Math. Comput. %D 2007 %V 25 %F Zhang2007 %0 Journal Article %T Existence for nonoscillatory solutions of second order nonlinear differential equations %A Y. Zhou %J J. Math. Anal. Appl. %D 2007 %V 331 %F Zhou2007 %0 Journal Article %T Oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients %A X. L. Zhou %A R. Yu %J Comput. Math. Anal. %D 2008 %V 56 %F Zhou2008 %0 Journal Article %T Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations %A Y. Zhou %A B. G. Zhang %A Y. Q. Huang %J Czechoslovak Math. J. %D 2005 %V 55 %F Zhou2005