Uniqueness theorem for ordinary differential equations with Hölder continuity

Uniqueness Theorem for Ordinary Differential Equations with Hölder Continuity

Uniqueness Theorems for Ordinary Differential Equations with Hölder Continuity

We establish some uniqueness results near 0 for ordinary differential equations of the type u(t) = f(u(t)) which satisfies u(0) = u′(0) = · · · = u(m−1)(0) = 0 and u(0) 6= 0 with m ≥ n. We also show that although f is not Lipschitz near 0, it is always Hölder continuous.

Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces

We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.

A Uniqueness Result for Ordinary Differential Equations with Singular Coefficients

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the order of singularities of the coefficients and provide examples to illustrate the results. 1. Results and examples Classical results on the existence and uniqueness of ordinary differential equations are mostly concerned with continuous coeffici...

A Uniqueness Result on Ordinary Differential Equations with Singular Coefficients

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the order of singularities of the coefficients and provide examples to illustrate the results. 1. Results and examples Classical results on the existence and uniqueness of ordinary differential equations are mostly concerned with continuous coeffici...