Results 141 to 150 of about 20,962 (157)

Monotone iterative technique for delay differential equations

Applicable Analysis, 1986
In proving existence of extremal solutions for delay differential equations, one usually assumes nondecreasing property on the function involved without which the proof breaks down. Our main purpose, in this paper, is to remove the monotone assumption by proving a new comparison result which is required in the analysis and which avoids the standard ...
V. Lakshmikantham, B.G. Zhang
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MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Acta Mathematica Scientia, 1998
The authors study the existence of minimal and maximal solutions to a class of nonlinear neutral delay differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and shown to converge to the extremal solutions to an initial value problem.
Jiang, Ziwen, Zhuang, Wan
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Monotone iterative techniques for nonlinear problems involving the difference of two monotone functions

Applied Mathematics and Computation, 2002
Consider the scalar initial value problem \((*) \;du/dt = f(t,u)+g(t,u), \;u(0)=0,\) under the condition that \(f\) is monotone increasing and \(g\) is monotone decreasing in \(u\). The authors prove a theorem on the convergence of a monotone iteration scheme provided coupled lower and upper solutions exist.
Bhaskar, T. G., McRae, Farzana A.
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An abstract monotone iterative technique

Nonlinear Analysis: Theory, Methods & Applications, 1997
On the Hilbert space \(H= L^2(\Omega)\), where \(\Omega \subset \mathbb{R}^n\) is open and bounded, the author considers a nonlinear equation (1) \(Lu= Nu\) where the linear operator \(L: D(L) \subset H \mapsto H\) satisfies the maximum principle \[ u \in D(L), \quad Lu+ \lambda u \geq 0\;\text{ on } \Omega \;\Longrightarrow \;u \geq 0\;\text{ on ...
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Monotone iterative techniques in ordered banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 1997
An abstract scheme is developed in order to obtain some results of existence and approximations of solutions for some different problems involving ordinary and functional differential equations. The machinery used is that of increasing operators in ordered Banach spaces.
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Monotone iterative technique for singular perturbation problem

Applied Mathematics and Computation, 2002
Consider the initial value problem \((*)\) \(dx/dt = f(t,x,y) + g(t,x,y)\), \(\varepsilon \, dy/dt = F (t,x,y) + G (t,x,y)\) with \(x,y \in \mathbb{R}\), \(0 < \varepsilon \leq \varepsilon_0 \ll 1,\) \((**)\) \(x(0) = x_0\), \(y(0) = y_0.\) Let \((\underline{x}_0 (t), \underline{y}_0 (t))\) and \((\overline{x}_0 (t), \overline{y}_0 (t))\) be ordered ...
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Monotone-iterative technique for decreasing mappings

Nonlinear Analysis: Theory, Methods & Applications, 2000
In continuation of his previous results [Nonlinear Anal., Theory Methods Appl. 30, No. 3, 1607-1616 (1997; Zbl 0892.34010)]the author develops the monotone-iterative technique for the case of decreasing \(\alpha\)-condensing operators in two partially ordered Banach spaces with normal cones.
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Monotone Convergence of the SOR-Newton Iterative Technique

SIAM Journal on Numerical Analysis, 1973
In this paper sufficient conditions are derived to insure monotone convergence of the SOR–Newton iterative technique. These conditions are derived by relating pointwise Lipschitz properties to the hypotheses of a general monotone convergence theorem.
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Monotone iterative technique for 1–dimensional stochastic differential equations

Stochastic Analysis and Applications, 1988
This paper is concerned with the construction of the minimal and maximal solutions of 1–dimensional stochastic differential equation of Ito's type under rather mild conditions for coefficients. To this, usual monotone iterative technique is used.
Ki Sik Ha, Jai Heui Kim
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Some Iterative Techniques For General Monotone Variational Inequalities

Optimization, 1999
In this paper, we use the Wiener-Hopf equations technique to suggest and analyze a new iterative method for solving general monotone variational ...
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