Existence of solutions to fourth-order differential equations with deviating arguments
Articles > Article · 2015
Authors: Mostepha Naceri, Ravi P. Agarwal, Erbil ÇETİN, El Haffaf Amir
Boundary Value Problems, Journal Indexed in SCI Expanded, International, WoS, 2015, vol 2015
DOI: 10.1186/s13661-015-0373-x
Summary
In this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form $u^{(4)}(t)+q(t)f(t,[u(t)],[u'(t)],[u''(t)],u'''(t))=0$ , $0< t<{+\infty}$ , with the boundary conditions $u(0)=A$ , $u'(0)=B$ , $u''(t)-au'''(t)=\theta(t)$ , $-\tau\leq{t}\leq 0$ ; $u'''(+\infty)=C$ . We present sufficient conditions for the existence of a solution between a pair of lower and upper solutions by using Schäuder’s fixed point theorem. Also, we establish the existence of three solutions between two pairs of lower and upper solutions by using topological degree theory. An important feature of our existence criteria is that the obtained solutions may be unbounded. We illustrate the importance of our results through two simple examples.