We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit functions theorem. This leads not only to an a priori proof of continuity, but also to an alternative, fully constructive existence proof.

In this work, an initial value problem is discussed for a fractional differential equation of variable-order. By means of some analysis techniques and Arzela-Ascoli theorem, existence result of solution is obtained; Using the upper solutions and lower solutions and monotone iterative method, uniqueness existence results of solutions are obtained.

This paper gives a new and short proof of existence and uniqueness of the Polubarinova-Galin equation. The existence proof is an application of the main theorem in Lin [2]. Furthermore, we can conclude that every strong solution can be approximated by many strong polynomial solutions locally in time.

The purpose of this paper is to give a stream-lined proof of the existence and uniqueness of a right-invariant mean on a CHART group. A CHART group is a slight generalisation of a compact topological group. The existence of an invariant mean on a CHART group can be used to prove Furstenberg’s fixed point theorem.

Existence, uniqueness, and a priori estimates for solutions are studied for stochastic parabolic Ito equations. An analog of the second fundamental inequality and the related existence theorem are obtained for backward stochastic parabolic Ito equation. AMS 1991 subject classification: Primary 60J55, 60J60, 60H10. Secondary 34F05, 34G10.

Using a general theory for evolution inclusions, existence and uniqueness theorems are obtained for weak solutions to a frictional dynamic contact problem for elastic visco-plastic material. An existence theorem in the case where the friction coefficient is discontinuous is also presented.

<abstract><p>The purpose of this study is to give some findings on the existence, uniqueness, and Hyers-Ulam stability solution an implicit coupled system impulsive fractional differential equations possessing a derivative Hadamard type. The existence uniqueness are obtained using fixed point theorem type Kransnoselskii. In keeping with this, many forms examined. Ultimately, support...

This paper is mainly concerned with feedback control systems governed by fractional impulsive evolution equations involving Riemann–Liouville derivatives in reflexive Banach spaces. We firstly give an existence and uniqueness result of mild solutions for the equations by applying the Banach’s fixed point theorem. Next, by using the Filippove theorem and the Cesari property, a new set of suffici...

By exploiting Perelman’s pseudolocality theorem, we prove a new compactness theorem for Ricci flows. By optimising the theory in the two-dimensional case, and invoking the theory of quasiconformal maps, we establish a new existence theorem which generates a Ricci flow starting at an arbitrary incomplete metric, with Gauss curvature bounded above, on an arbitrary surface. The criterion we assert...