coupled lower and upper solutions
Generalized Quasilinearization Using Coupled Lower and Upper Solutions for Periodic Boundary Value Problem of an Integro Differential Equation
... Abstract. In this paper we first develop the method of generalized quasilinearization for initial value problem of an integro differential equation and then use it to develop quasilinearization for the periodic boundary ...
14
Causal difference equations with upper and lower solutions in the reverse order
... of lower and upper solutions v(k), w(k) and the monotone iterative technique, we testify the existence of the extremal solutions for (1) and (2) with v(k) ≥ ...of coupled lower ...
15
Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equation
... Using coupled lower and upper solutions we develop the generalized monotone iterative technique to solve Caputo fractional integro-differential equation of order q with periodic boundary ...
14
E x t e nde d M o no t o neM e t ho ds f o r Hy pe r bo l i c P r o bl e m si n T hr e eV a r i a bl e s
... natural lower-upper solutions and the coupled lower-upper solutions, we derive monotone it- erative schemes in a unified ...
5
Stability of periodic solutions of first order difference equations lying between lower and upper solutions
... Our purpose is to ensure the stability of at least one periodic solution of a first-order di ff erence equation. We will prove such result by using a monotone nondecreasing oper- ator. In this case, the defined operator ...
11
Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces
... of lower and upper solutions coupled with the monotone iterative technique, we construct two monotone iterative sequences and prove that the sequences monotonically converge to the minimal and ...
14
Method of upper lower solutions for nonlinear system of fractional differential equations and applications
... Now-a-days the theory of fractional differential equations have been occupying an importance place in science and tech- nology.Fractional differential equations have been widely used for modeling various processes in ...
6
UPPER AND LOWER SOLUTIONS METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS
... [18] K. Shah, R.A. Khan, Iterative solutions to a coupled system of nonlinear fractional differential equation, J. Frac. Calc. Appl., 7, No 2 (2016), 40–50. [19] G. Wang, S. Liu, R.P. Agrawal, L. Zhang, ...
14
An Overview of the Lower and Upper Solutions Method with Nonlinear Boundary Value Conditions
... As far as the author is aware, the first reference in which this problem has been studied in combination with the method of lower and upper solutions is due to De Coster in 50, who considers 3.1 ...
18
Monotone iterative technique for causal differential equations with upper and lower solutions in the reversed order
... (coupled) upper and lower solutions in the reversed order to discuss the existence of extremal solutions (quasi-solutions) for causal differential equations with nonlinear ...
14
Initial value problems for fractional differential equations involving Riemann-Liouville derivative
... Existence results obtained by Yaker and Koksal are improved for the class of continuous functions. Monotone method coupled with lower and upper solutions is developed for the initial value ...
9
Extremal mild solutions for impulsive fractional evolution equations with nonlocal initial conditions
... technique coupled with the method of upper and lower solutions, we construct two groups of monotone iterative sequences, and then prove these sequences monotonically converge to the maximal ...
12
Periodic boundary value problems for second-order impulsive integro-differential equations with integral jump conditions
... technique coupled with the method of upper and lower solu- tions has been used to study the existence of extremal solutions of periodic boundary value problems for second-order impulsive ...
21
Monotone iterative method for differential systems with coupled integral boundary value problems
... of upper and lower solutions and the monotone iterative technique, we investigate the differential systems with coupled integral boundary value ...of solutions of the given ...
9
Nonlinear Boundary Value Problem of First Order Impulsive Functional Differential Equations
... extremal solutions and unique solution in Section 3 by using the method of upper and lower solutions coupled with monotone iterative ...
14
Lower and upper estimates of solutions to systems of delay dynamic equations on time scales
... sidered equations to get a bounded solution y ∈ . The reason is that in a delay case the history of solutions plays an important role and influences conditions for points, which are strict egress with respect to ...
14
The unique solution for periodic differential equations with upper and lower solutions in reverse order
... the upper and lower solution method together with the iterative technique is a powerful tool for proving the existence results for boundary value problems (see [–] and the references ...the upper ...
12
The method of upper and lower solutions to impulsive differential equations with integral boundary conditions
... Recently, some well-known works, such as Hao et al. [], Zhang et al. [] and Ding and Wang [], deal with impulsive differential equations with integral boundary conditions. However, most of these results are obtained ...
11
The method of lower and upper solutions for the cantilever beam equations with fully nonlinear terms
... of solutions to the fully fourth- order nonlinear boundary value problem ...symmetric solutions when f satisfies some range conditions dependent upon three positive parameters a, b and ...of lower and ...
16
Dynamics of a predator–prey system with three species
... wave solutions of parabolic equations; we refer to Volpert et ...wave solutions; we re- fer to some important results by Dunbar [9–11], Gardner and Smoller [16], Gardner and Jones [15], Chen et ...
25