Second-order differential equations with deviating arguments

Abstract

This paper deals with boundary value problems for second-order differential equations with deviating arguments. Some sufficient conditions are formulated under which such problems have quasisolutions or a unique solution. A monotone iterative method is used. Examples with numerical results are added to illustrate the results obtained.

Extremal solutions of Cauchy problems for abstract fractional differential equations

“…Recently, Zhou and Jiao [28] discussed the existence of extremal solutions for discontinuous fractional functional differential equations involving Caputo derivative and applied the hybrid fixed point methods to study such problems. However, both the results obtained in [11] and [28] hold only in finite dimensional spaces.…”

“…On the other hand, the existence results of extremal solutions for fractional differential equations with deviating arguments involving Riemann-Liouville derivative has been reported by Jankowski [11]. To deal with the problem of the existence of extremal solutions, Jankowski applied the well known monotone iterative technique.…”

Quasi-solutions for generalized second order differential equations with deviating arguments

“…, w(y 0 , z 0 ))) + 1 a g 1 (y 0 (0), w(y 0 , z 0 )) − 1 a g 1 (y 0 (0), w(y 0 , z 0 )) = y 0 (0) − z 0 (0) + 1 a (g 1 (y 0 (0), w(y 0 , z 0 )) − g 1 (y 0 (0), w(y 0 , z 0 ))) + 1 a (g 1 (z 0 (0), w(y 0 , z 0 ) − g 1 (y 0 (0), w(y 0 , z 0 ))) (7) and (8). By the same way we can show that p(T ) 0.…”

“…Before, usually periodical boundary conditions where assumed, or like in [7] and [8] for functions g 1 and g 2 defined by The plan of this paper is as follows. In Sections 2 and 3 we introduce necessary tools and definitions.…”

Analysis of the Sign of the Solution for Certain Second-Order Periodic Boundary Value Problems with Piecewise Constant Arguments

“…Here, the functional dependence considered is the greatest integer function. In [16], the authors consider boundary value problems for second-order differential equations with deviating arguments and, in [17], the uniqueness issue is addressed for second-order linear functional differential equations.…”