A new three-term conjugate gradient-based projection method for solving large-scale nonlinear monotone equations [PDF]
Mathematical Modelling and Analysis, 2019 A new three-term conjugate gradient-based projection method is presented in this paper for solving large-scale nonlinear monotone equations. This method is derivative-free and it is suitable for solving large-scale nonlinear monotone equations due to its
Mompati Koorapetse, Professor Kaelo
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New fixed points of mixed monotone operators with applications to nonlinear integral equations. [PDF]
PLoS ONEIn this paper, first we recall and present some basic results about cone and partial order within the framework of Banach spaces. Next, by means of the properties of cone and monotone iterative techniques, some new fixed point theorems of mixed monotone ...
Shaoyuan Xu +3 more
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A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations
Mathematics, 2020 The goal of this paper is to extend the modified Hestenes-Stiefel method to solve large-scale nonlinear monotone equations. The method is presented by combining the hyperplane projection method (Solodov, M.V.; Svaiter, B.F.
Zhifeng Dai, Huan Zhu
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On variational nonlinear equations with monotone operators [PDF]
Advances in Nonlinear Analysis, 2020 Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations.
Galewski Marek
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Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems [PDF]
Abstract and Applied Analysis, 2020 Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses.
Mathew O. Aibinu +2 more
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Mathematical and Computational Applications, 2020 A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations.
Aliyu Muhammed Awwal +4 more
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Monotone Solutions of Second-Order Nonlinear Differential Equations
Applied Mathematics Letters, 2000 Necessary and sufficient conditions are obtained for the existence of a positive nondecreasing solution to equations of the form \[ [r(t)(y'(t))^{\alpha }]'+q(t)(y(t))^{\alpha }=0, \] where \(\alpha \) is a positive number and \(r, q\) are continuous functions. As applications, some comparison theorems are derived.
Wan-Tong Li
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Algebraic Systems with Positive Coefficients and Positive Solutions
Mathematics, 2022 The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients.
Ana Maria Acu +2 more
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semilinear wave equation with non-monotone nonlinearity
Electronic Journal of Differential Equations, 2023 We prove the existence of weak solutions to a semilinear wave with non-monotone asymptotically linear nonlinearity when the forcing is dominated by a trigonometric polynomial.
José F. Caicedo +3 more
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Monotone method for Riemann-Liouville multi-order fractional differential systems [PDF]
Opuscula Mathematica, 2016 In this paper we develop the monotone method for nonlinear multi-order \(N\)-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders \(q_i\) where \(0 \lt q_i \lt 1\).
Zachary Denton
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