In this paper, existence and uniqueness of solution to two-point boundary value for two-sided fractional differential equations involving Caputo fractional derivative is discussed, by means of the Min-Max Theorem.

An existence and uniqueness theorem for the nonlinear complementarity problem over closed convex cones in a reflexive real Banach space is established, using perturbations of solutions of variational inequalities and monotonicity methods.

FOLLOING OUR PREVIOS PROJECT [1], WE ARE GOING TO PROVE THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE SPECTRAL PROBLEM IN THIS PROJECT.FIRST,WE HAVE PROVEN THE UNIQUENESS OF THE SOLUTION THEN TO PROVE THE EXISTRNCE WE CONSTENSS OF THE ADJOINT PROBLEM CORRESPONDING TO THIS SPECTRAL PROBLEM NEXT THE UNIQUESS OF THE ADJOINT PROBLEM IS THE EXISTENCE OF THE MAIN PROBLEM AS DISCUSSED BY[2] AND ...

In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.

We prove an existence and uniqueness theorem for backward stochastic di erential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.

By using Mawhin–Manásevich continuation theorem, some new sufficient conditions for the existence and uniqueness of periodic solutions of Duffing type p-Laplacian differential equation are established, which are complement of previously known results. © 2007 Elsevier Inc. All rights reserved.

In this article we consider the existence, uniqueness and positivity of a first order non-linear periodic differential equation. The main tool employed is the Krasnosel’skĭı’s fixed point theorem for the sum of a completely continuous operator and a contraction.

1 Conditional expectation 3 1.1 Discrete case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Existence and uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Product measure and Fubini’s theorem . . . . . . . . . . . . . . . . . . . . . 11 1.4 Examples of conditional expectation . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Gaussian ...

This work is concerned with the existence and uniqueness of positive solutions for Neumann boundary value problems of second order impulsive differential equations. The result is obtained by using a fixed point theorem of generalized concave operators. MSC: 34B18; 34B37

We apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence uniqueness of their solutions. Next, we compute optimum error estimate. The mentioned process i.e., stabilization by a control function finding an approximation for functional equation is called HUR stability. use fixed point technique derived from alternative theore...