Very often existence and uniqueness theorems are combined in statements of the ... For first-order differential equations the answers to the existence and ...
Existence and Uniqueness of Solutions of Nonlinear Equations · 1) may have more than one solution on a larger interval that contains . · 2) would have a unique ...
10 , 343–359 ( 1991) Cite this article 240 Accesses 42 Citations Metrics Abstract An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure.
obtain the solution by an application of the Contraction Mapping Theorem that was discussed ... unique solution of the initial value problem of the ODE.
Open Access Published by De Gruyter Open Access December 19, 2017. EXISTENCE AND UNIQUENESS THEOREMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ...
Bu, C. (2020) Local Existence and Uniqueness Theorem for a Nonlinear Schrödinger Equation with Robin Inhomogeneous Boundary Condition. Journal of Applied Mathematics and Physics, 8, 464-469. doi: 10.4236/jamp.2020.83036.
The Existence and Uniqueness Theorem tells us that the integral curves of any differential equation satisfying the appropriate hypothesis, cannot cross. If the curves did cross, we could take the point of intersection as the initial value for the differential equation.
Existence and Uniqueness of Solutions of Nonlinear Equations Although there are methods for solving some nonlinear equations, it’s impossible to find useful formulas for the solutions of most. Whether we’re looking for exact solutions or numerical approximations, it’s useful to know conditions that imply the existence and uniqueness of solutions of initial value problems for …
25.09.2018 · They are also both valid for all real numbers. I am told, however, that despite this, the two solutions do not contradict the nonlinear existence and uniqueness theorem. How could this be? For reference, the differential equation is d y / d x = 1 2 ( − x + ( x 2 + 4 y) 1 2), and the initial value given is y ( 2) = − 1.
18.06.2013 · In the present paper, a system of nonlinear impulsive differential equations with two-point and integral boundary conditions is investigated. Theorems on the existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.