In this article, we study sufficient conditions for existence and uniqueness of positive solutions to the following coupled system of fractional order differential equations with antiperiodic boundary conditions { cDαu(t)+ f (t,v(t), Dα−1v(t)) = 0, cDβ v(t)+g(t,u(t), Dβ−1u(t)) = 0, 0 < t < 1, u(0) = −u(1),v(0) = −v(1), Du(0) = −Dpu(1), Dv(0) = −Dqv(1), where 1 < α ,β 2,α − p 1,β − q 1 and 0 < p...

Existence and approximation of best proximity points is an interesting topic for which one can see [2, 3, 4, 6, 5] for more information. Another extension of Banach contraction principle was given by Nieto and Rodriguez-Lopez in partially ordered metric spaces [9]. They proved some fixed point theorems in partially ordered sets in order to show the existence and uniqueness for a first-order ord...

In this paper, we prove the existence of solutions for an anti-periodic boundary value problem of nonlinear impulsive fractional differential equations by applying some known fixed point theorems. Some examples are presented to illustrate the main results.

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

An analytic solution is presented describing ̄ow to a drain in a semi-in®nite domain bounded by a leaky layer of constant thickness. The solution is developed by applying the method of images to two parallel boundaries: an inhomogeneity boundary and an equipotential boundary. It is then demonstrated that the solution for the problem with the leaky layer approximated by a leaky boundary (a mixed...

The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.

As we have seen in Chapter 2, the partition function of the Ising model on a planar graph G with positive boundary conditions is proportional to the even subgraph generating function ZG⇤(x), where G⇤ is the weak dual of G and x is the weight vector defined by the low-temperature expansion. Similarly, the partition function of the model with free boundary conditions is proportional to ZG(x), whe...

In this paper we prove the existence of weak periodic solutions for a nonlinear parabolic equations with the Robin periodic boundary condition. The aim will be achieved by reformulating the problem in abstract form and applying some results of the maximal monotone mapping theory joint with the Schauder fixed point theorem.

*Correspondence: [email protected] 1School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan 410075, P.R. China 2School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, P.R. China Full list of author information is available at the end of the article Abstract By using Schauder’s fixed poin...

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. By using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are ...