In this paper the existence of unique positive solutions for system (p,q,r)-Lapalacian Sturm-Liouville type two-point fractional order boundary vaue problems is established by an application n-fixed point theorem ternary operators on partially ordered metric spaces.

Deguire and Lassonde [P. Deguire, M. Lassonde, Familles sélectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261–269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obt...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

We derive the linear elastic Cosserat shell model of order O(h5) in thickness h. To this aim, we linearise geometrically nonlinear established previously. Using Korn-type inequalities for shells, coercivity energy functional and Lax-Milgram theorem, prove existence uniqueness weak solutions to equilibrium equations.

In this paper, we establish an asymptotic existence theorem for group divisible designs of type mn with block sizes in any given set K of integers greater than 1. As consequences, we will prove an asymptotic existence theorem for frames and derive a partial asymptotic existence theorem for resolvable group divisible designs. © 2006 Elsevier Inc. All rights reserved.

Abstract In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with boundary conditions is given, which can cover classical linear conditions, such as the homogeneous Dirichlet or Neumann condition. The advantage our over ones lies in fact that it enables us to compare two solutions satisfying different types conditions. As an application theorem, w...

In this paper, we study the existence of solutions for fractional evolution equations with nonlocalconditions. These results are obtained using Banach contraction xed point theorem. Other resultsare also presented using Krasnoselskii theorem.