We consider a system of differential equations possessing a family of T -periodic solutions and subjected to a T -periodic Lipschitz small perturbation. We prove the existence and uniqueness of a T -periodic solution of the perturbed system by means of a Lipschitz generalization of the Lyapunov–Schmidt reduction method. When the perturbation is continuously differentiable our result coincides w...

‎the purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces‎. ‎also‎, ‎we present a result on the existence and uniqueness of coupled common fixed points‎. ‎the results presented in the paper generalize and extend several well-known results in the literature‎.

in this paper, we are interested to study the sine-gordon equation in generalized functions theory introduced by colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the colombeau algebra). then we study the association concept with the classical solution.

We prove a result of uniqueness of the entropy weak solution to the Cauchy problem for a class of nonlinear hyperbolic systems of conservation laws, that includes in particular the p-system of isentropic gas dynamics. Our result concerns weak solutions satisfying the, as we call it, Wave Entropy Condition or WEC, for short, introduced in this paper. The main feature of this condition is that it...

This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

In this paper we use the continuation theorem of coincidence degree theory and analysis techniques. We establish the existence and uniqueness of a T-periodic solution for the third-order delay differential equation with two deviating arguments. A new result on the existence and uniqueness of a periodic solution of this equation is obtained. In addition an example is given to illustrate the main...

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.