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An ordinary differential equation in nonlinear programming
Nonlinear Analysis: Theory, Methods & Applications, 1990It is proved that the initial value problem of an ordinary differential equation \(x'=P(x,g'(x)),\quad x(0)=x_ 0,\) arising in nonlinear programming, has a unique solution under certain assumptions.
Hassan, Nizar, Rzymowski, Witold
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Ordinary Differential Equations with Nonlinear Boundary Conditions
gmj, 2002Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.
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On some nonlinear ordinary differential equations with advanced arguments
Nonlinear Analysis: Theory, Methods & Applications, 2003The authors consider the following nonlinear differential equation with advanced argument \[ y'(t)= [y(\beta t)]^{1/\beta},\tag{1} \] with \(t\geq 0\) and \(\beta> 1\). By making use of the technique of lower and upper solutions, they classify the solutions of (1) (those that satisfy the initial condition \(y(0)= y_0\) and a certain growth condition ...
Antoni Augustynowicz +2 more
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On the asymptotic behavior of solutions to nonlinear ordinary differential equations
Asymptotic Analysis, 2007We discuss a number of issues important for the asymptotic integration of ordinary differential equations. After developing the tools required for application of the fixed point theory in the investigation, we present some general results about the long-time behavior of solutions of n-th order nonlinear differential equations with an emphasis on the ...
Agarwal, Ravi P. +4 more
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A method for solution of nonlinear ordinary differential equations
Ukrainian Mathematical Journal, 1995The author proposes a scheme for solving the problem \[ u''+2u'/x+\beta ^2u^\nu =0,\;u(0)=0, \quad u'(0)=0. \] After rather cumbersome manipulations he obtains the integral equation \[ u(x)=1+\lambda ^{-1}\int_{0}^{x}\Biggl[(c\lambda +\xi)\psi [a](\xi)-\varepsilon ^{-\mu }(c\xi)^{-1}\int_{0}^{\xi }\zeta ^2a(\zeta) d\zeta \Biggr]d\xi \] with \(a ...
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On growing solutions of nonlinear ordinary differential equations
Mathematical Notes, 1997The author considers the solutions of an \(m\)th-order differential equation \[ w^{(m)}= Q(r,w, \dots, w^{(m-1)}), \] satisfying the condition: \[ w^{(m-i)}(r_*)> {t_*\over(i-1)!} r_*^{i-1}, \quad \text{for }i=1,2, \dots, m. \] If \(Q\) is a Carathéodory-type function on \([r_*,+\infty [\times \mathbb{R}^m\), such that for some \(k\in\{0,1, \dots, m-2\}
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Stability Criteria for Nonlinear Ordinary Differential Equations
Journal of the Society for Industrial and Applied Mathematics Series A Control, 1963The main results of this work are three sufficient conditions for the (1) stability, (2) uniform asymptotic stability in the large and (3) instability, of the equilibrium point $x = 0$ of the system of differential equations: $\dot x = f(t,x)$, $f(t,0) = 0$. Stated roughly these conditions are: The point $x = 0$ is (1) stable if $x'f(t,x)$ is a concave
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On Nonlinear Systems of Ordinary Differential Equations
1988The paper gives some analytical representations and numerical methods for the solutions of systems of ordinary differential equations with emphasis of the formal side, using the connection to the linear partial differential equations in the case first mentioned.
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Piecewise homotopy methods for nonlinear ordinary differential equations
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Exact linearization of nonlinear ordinary autonomous differential equations
Programming and Computer Software, 2000Many methods for finding exact solutions to nonlinear ordinary differential equations (ODE) are based on certain euristic rules. The author suggested a newexact linearization method that provides an algorithmic procedure for constructing exact solutions for some important classes of ODEs [1].
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