In this paper, we consider a class of nonlinear fuzzy integral equations of fractional order. The existence and uniqueness of solutions are established by the generalized Schauder theorem and contraction mapping principle.

We have investigated the existence and uniqueness solutions of the nonlinear fractional differential equation of an arbitrary order with integral boundary condition. The result is an application of the Schauder fixed point theorem and the Banach contraction principle.

We define Strebel differentials for stable complex curves, prove the existence and uniqueness theorem that generalizes Strebel’s theorem for smooth curves, prove that Strebel differentials form a continuous family over the moduli space of stable curves, and show how this construction can be applied to clarify a delicate point in Kontsevich’s proof of Witten’s conjecture.

n this paper, we study the existence and uniqueness of an intuitionistic fuzzy solution for semi-linear integro-differential equations with non-local conditions using Banach fixed point theorem. Theorem on these problems nonlocal are presented under certain assumptions. Finally, example is established to illustrate effectiveness

Using a fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to three-point boundary value problems for second order impulsive differential equations. MSC: 34B15; 34B10; 34B18

Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.

Mean curvature flow evolves isometrically immersed base Riemannian manifolds M in the direction of their mean curvature in an ambient manifold M̄ . We consider the classical solutions to the mean curvature flow. If the base manifold M is compact, the short time existence and uniqueness of the mean curvature flow are well-known. For complete noncompact isometrically immersed hypersurfaces M (unif...

We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.

We prove an existence and uniqueness theorem for stationary solutions of the inviscid Burgers equation on a segment with random boundary conditions. We also prove exponential convergence to the stationary distribution.

We show that the fundamental theorem of immersion theory admits a Poincaré duality space analogue. Along the way, we obtain new homotopy theoretic proofs of the existence and uniqueness of the Spivak normal fibration of a closed Poincaré space.