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.

In this article, we prove uniqueness of symmetric positive solutions of the variational ODE system −w′′ + aw − wv = 0 −v′′ + bv − w2 2 = 0, where a and b are positive constants.

Smale’s 17th Problem asks “Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average [for a suitable probability measure on the space of inputs], in polynomial time with a uniform algorithm?” We present a uniform probabilistic algorithm for this problem and prove that its complexity is polynomial. We thus obtain a partial positive solution to Smale 17th P...

The paper studies the Bardeen{Cooper{Schrieeer energy gap equation at nite temperatures. When the kernel is positive representing a phonon-dominant phase in a superconductor, the existence and uniqueness of a gap solution is established in a class which contains solutions obtainable from bounded domain approximations. The critical temperatures that characterize superconducting-normal phase tran...

Applying positive joint torque feedback in direct drive motor systems reduces the eeect of external load torques. This is most beneecial when accurate position tracking is required in the presence of large disturbances or for complex loads as found in robotic manip-ulators. We formulate the problem of torque feedback in the presence of actuator dynamics. The problem of nding the optimal torque ...

In this paper, an efficient iterative method is presented to solve a new nonlinear matrix equation * r X A X A I   with real matrices and r 1  . Some properties of the positive definite solutions for the nonlinear matrix equation are derived. Moreover, necessary and sufficient conditions for the existence of the positive definite solutions are derived. The error estimation of the iterative m...

Copyright © 2013 X. Guo and D. Shang.This is an open access article distributed under theCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The fuzzy matrix equations ?̃?⊗?̃?⊗?̃? = ?̃? in which ?̃?, ?̃?, and ?̃? arem×m, n×n, andm×n nonnegative LR fuzzy numbers matrices, respectively, are invest...

In this paper, the method of upper and lower solutions and the Schauder fixed point theorem are used to investigate the existence and uniqueness of a positive solution for a class of nonlinear fractional differential equations with non-monotone term. An example is also given to illuminate our results. 2000 MSC: 34B15 • 34B18

this paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by topsis method. topsis method is technique for order preference by similarity to ideal solution. topsis is one of the renowned methods for classical multi-criteria decision-making (mcdm) problems that defines the positive ideal solution and negative ideal solution...

‎In this paper‎, ‎we formulate the sixth-order boundary value problem as Fredholm integral equation by finding Green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎Also nonexistence results are obtained‎. ‎An example is given to illustrate the results of paper‎.