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1
Content available Region of existence of multiple solutions for a class of robin type four-point bvps
Verma Amit K., Urus Nazia, Agarwal Ravi P.
Opuscula Mathematica
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2021
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Vol. 41, no. 4
571--600
EN
This article aims to prove the existence of a solution and compute the region of existence for a class of four-point nonlinear boundary value problems (NLBVPs) defined as [formula] where I = [0, 1], 0 < ξ≥ η < 1 and λ 1 ,λ > 0. The nonlinear source term [formula] is one sided Lipschitz in u’ with Lipschitz constant L 1 and Lipschitz in u', such that [formula]. We develop monotone iterative technique (MI-technique) in both well ordered and reverse ordered cases. We prove maximum, anti-maximum principle under certain assumptions and use it to show the monotonic behaviour of the sequences of upper-lower solutions. The sufficient conditions are derived for the existence of solution and verified for two examples. The above NLBVPs is linearised using Newton’s quasilinearization method which involves a parameter k equivalent to max [formula]. We compute the range of k for which iterative sequences are convergent.
2
Content available Extremal solutions to a coupled system of nonlinear fractional differential equations with ψ–Caputo fractional derivatives
Derbazi Choukri, Baitiche Zidane, Benchohra Mouffak, Graef John R.
Journal of Mathematics and Applications
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2021
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Vol. 44
19--34
EN
Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the ψ–Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.
3
Content available remote Monotone iterative technique for non-autonomous semilinear differentia equations with nonlocal condition
Meraj Arshi, Pandey Dwijendra Narain
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
29--39
EN
The objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered complete norm space X, using evolution system and measure of noncompactness.
4
Content available remote The method of quasilinearization for system of hyperbolic functional differential equations
Karpowicz A.
Commentationes Mathematicae
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2008
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Vol. 48, [Z] 2
155-168
EN
We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations. [zob. pełny tekst: http://www.staff.amu.edu.pl/~commath/papers/482/4825.pdf]
5
Content available remote Impulsive functional-differential equations of first order
Skóra L.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
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Vol. 47, [Z] 2
207-219
EN
In this paper we present some existence results for impulsive functionaldifferential equations of first order.
6
Content available Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type
Zabawa T.S.
Opuscula Mathematica
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2005
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Vol. 25, no. 2
333-343
EN
The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and uper functions.
7
Content available remote Monotone iterative techniques for impulsive retarded differential-functional equations systems
Skóra L.
Demonstratio Mathematica
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2004
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Vol. 37, nr 1
101--113
EN
In this paper, the monotone iterative method is applied to impulsive retarded functional-differential problem. The problem is also discussed in case we abandon the monotone method and start directly with the equivalent integral equation.
8
Content available remote Monotone iterative method for differential systems with impulses and anti-periodic boundary condition
Skóra L.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2002
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[Z] 42(2)
237-249
EN
In the paper we present some results on the existence of the solutions of first-order impulsive ordinary differential systems with anti-periodic boundary conditions.
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