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Multivalued Differential Equations and Ordinary Differential Equations
SIAM Journal on Applied Mathematics, 1970(E) e F(x, t), where F is upper semicontinuous, from known results in the theory of ordinary differential equations. This will be accomplished by showing that, for any F upper semicontinuous and convex, it is always possible to "approximate" the multivalued differential equation (E) by appropriately chosen ordinary differential equations. This would be
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The Mathematical Gazette, 1945
1. We deal with the equationwhere ψ(ωt)is continuous, periodic in t with period 2π/ω a, k2 are real and positive, and A stable (bounded) solution was given by Erdélyi in 1934 employing a complicated transformation and integral equations.We shall obtain this solution by an elementary method, thereby reducing the analysis to one-third of its former ...
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1. We deal with the equationwhere ψ(ωt)is continuous, periodic in t with period 2π/ω a, k2 are real and positive, and A stable (bounded) solution was given by Erdélyi in 1934 employing a complicated transformation and integral equations.We shall obtain this solution by an elementary method, thereby reducing the analysis to one-third of its former ...
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geometry of differential equations
Journal of Soviet Mathematics, 1983This paper contains a survey of papers on the geometry of differential equations, which appeared no earlier than 1972, continuing the general survey (RZhMat, 1974, 11A800), and considers in more detail a special cycle of investigations of the geometry of systems of partial differential equations, distinguished by the presence of practical applications.
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1966
Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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A Differential-Difference Equation
SIAM Journal on Mathematical Analysis, 1987Wimp shows that the hypergeometric polynomials \[ P_ n(z)=_{p+2}F_{p+1}(-n,n+\lambda,a_ p;b_{p+1};z),\quad n=0,1,...\quad, \] satisfies a certain differential-difference equation. Here we show that all ''common'' solutions to the standard differential equations and the standard difference equation satisfied by the \(P_ n(z)\) also satisfy the above ...
Fields, Jerry L., Al-Salam, Waleed A.
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2011
This chapter introduces numerical methods that can be used on problems that are too hard to solve by standard algebra, such as finding roots of complicated equations. It demonstrates numerical methods for solving a first-order ordinary differential equations (ODE) with an initial condition.
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This chapter introduces numerical methods that can be used on problems that are too hard to solve by standard algebra, such as finding roots of complicated equations. It demonstrates numerical methods for solving a first-order ordinary differential equations (ODE) with an initial condition.
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On the Stability of Differential Equations
SIAM Journal on Control, 1972A polynomial is said to be of type $(p_1 ,p_2 ,p_3 )$ relative to any directed line in the complex plane if it has $p_1 $ zeros to the left of, $p_2 $ on, and $p_3 $ to the right of the line.
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