Nonoscillatory solutions for higher-order nonlinear neutral delay differential equations

作者：Liu, Zeqing; Jia, Ming; Ume, Jeong Sheok^*; Kang, Shin Min

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014, 2014(1): 302.

DOI：10.1186/1029-242X-2014-302

• higher-order nonlinear neutral delay differential equation
• uncountably many bounded nonoscillatory solutions
• Krasnoselskii fixed point theorem
• Schauder fixed point theorem

This paper deals with the solvability of the higher-order nonlinear neutral delay differential equation d(n)/dt(n) [x(t) + p(t) x(t -tau)] + (-1)(n+1) Sigma(m)(i=1) q(i)(t) x (alpha(i)(t)) + (-1)(n+1)f (t, x(beta(1)(t)),..., x(beta(l)(t))) = r(t), t >= t(0), where tau > 0, n, m, l is an element of N, p, r, q(i), alpha(i), beta(j) is an element of C([t(0),+infinity), R), and f is an element of C([t(0),+infinity) x R-l, R) satisfying lim(t ->+infinity) alpha(j)(t) = lim (t ->+infinity) beta(j)(t) = +infinity, i is an element of {1, 2,..., m}, j is an element of {1, 2,..., l}. With respect to various ranges of the function p, we investigate the existence of uncountably many bounded nonoscillatory solutions for the equation. The main tools used in this paper are the Krasnoselskii and Schauder fixed point theorems together with some new techniques. Six nontrivial examples are given to illustrate the superiority of the results presented in this paper.

• 出版日期2014-8-19
• 单位辽宁师范大学