A New Sixth Order Method for Nonlinear Equations in R [PDF]
The Scientific World Journal, 2014 A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x0, the method generates a sequence of iterates converging to the root.
Sukhjit Singh, D. K. Gupta
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Liouville type theorems for the system of fractional nonlinear equations in R + n ${R^{n}_{+}}$
Journal of Inequalities and Applications, 2016 In this paper we consider the following system of fractional nonlinear equations in the half space R + n ${R^{n}_{+}}$ : 1 { ( − Δ ) α 2 u 1 ( x ) = x n γ u 1 α 1 ( x ) u 2 β 1 ( x ) , x ∈ R + n , ( − Δ ) α 2 u 2 ( x ) = x n γ u 1 α 2 ( x ) u 2 β 2 ( x )
Zhaohui Dai, Linfen Cao, Pengyan Wang
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Journal of Numerical Analysis and Approximation Theory, 2021 We develop a new families of optimal eight--order methods for solving nonlinear equations. We also extend some classes of optimal methods for any suitable choice of iteration parameter.
Tugal Zhanlav, Otgondorj Khuder
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Comparison of some optimal derivative-free three-point iterations
Journal of Numerical Analysis and Approximation Theory, 2020 We show that the well-known Khattri et al. methods and Zheng et al. methods are identical. In passing, we propose a suitable calculation formula for Khattri et al. methods.
Thugal Zhanlav, Khuder Otgondorj
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p-Laplacian Equations in R + N with Critical Boundary Nonlinearity [PDF]
Mathematics, 2020 In this paper, we consider the following p-Laplacian equation in R+N with critical boundary nonlinearity. The existence of infinitely many solutions of the equation is proved via the truncation method.
Xu Miao, Junfang Zhao, Xiangqing Liu
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Solutions with multiple peaks for nonlinear Kirchhoff equations on R^3
Annales Fennici Mathematici, 2023 In this paper, we mainly investigate the following nonlinear Kirchhoff equation \(-\left(\epsilon^2 a+\epsilon b\int_{\mathbb{R}^3}|\nabla u|^2\right)\Delta u +u =Q(x)u^{q-1}\), \(u>0\), \(x\in\mathbb{R}^{3}\), \(u\to 0\), as \(|x|\to +\infty\), where \(a,b>0\) are constants, \(2<q<6\), and \(\epsilon>0\) is a ...
Chen, Hong, Hua, Qiaoqiao
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Nonlocal Nonlinear Schrödinger Equations in R 3 [PDF]
Archive for Rational Mechanics and Analysis, 2013 This paper studies a class of nonlocal nonlinear Schrodinger equations in R 3 , which occurs in the infinite ion acoustic speed limit of the Zakharov system with magnetic fields in a cold plasma. The magnetic fields induce some nonlocal effects in these nonlinear Schrodinger systems, and the main goal of this paper is to understand these effects.
Gan, Zaihui, Zhang, Jian
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Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations [PDF]
Mathematica Moravica, 2022 In this paper, we shall discuss the existence and uniqueness of solutions for a nonlinear anti-periodic boundary value problem for fractional impulsive differential equations involving a Caputo-Fabrizio fractional derivative of order r ∈ (0, 1).
Benyoub Mohammed, Belghaba Kacem
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A nonlinear eigenvalue problem in $\Bbb R$ and multiple solutions of nonlinear Schrödinger equation
Advances in Differential Equations, 2002 Consider the nonlinear Sturm-Liouville eigenvalue problem \[ u''-Q(x)u+\lambda(Mu+f(u))=0,\quad x\in\mathbb R,\quad \lim_{| x| \to\infty}u(x)=\lim_{| x| \to\infty}u'(x)=0, \] where the potential \(Q\) is positive and coercive, the function \(f(s)\) behaves like \(s^p,p>1\), \(M\) is positive constant and \(\lambda\) is a positive parameter.
Felmer, P., Torres, J. J.
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The spectrum in $R$ and $R^2$ of nonlinear elliptic equations with positive parameters [PDF]
Rocky Mountain Journal of Mathematics, 2015 In this paper we study the spectrum in $\R$ and $\R^2$ of nonlinear elliptic equations with positive parameters in their nonlinear part. In order to investigate the spectrum in these specific cases, we introduce the monotone method which is an extension of the upper and lower solution methods.
Trejo, Imelda, Felipe, Raúl
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