in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0

We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x) = F(G(x), . . . , G(x)), where F is a given function of n real variables. We provide necessary and sufficient conditions on F for the existence and uniqueness of solutions. When F is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing...

Let A be an adjacency matrix of a tree T with n vertices. Conditions are determined for the existence of a fixed permutation matrix P that maximizes the quadratic form xtP tAPx over all nonnegative vectors x with entries arranged in nondecreasing order. This quadratic form problem is completely solved, and its answer leads to a corresponding solution for the problem of determining conditions fo...

Motivated by applications in online advertising, we consider a class of maximization problems where the objective is function sequence actions and running duration each action. For these problems, introduce concepts sequence-submodularity sequence-monotonicity, which extend notions submodularity monotonicity from functions defined over sets to sequences. We establish that if sequence-submodular...

This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn f xn−2 /g xn−1 , n ∈ N0, where f, g ∈ C 0,∞ , 0,∞ . It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n−1} are eventually monotone. For the case when f x α βx and g satisfies the conditions g 0 1, g is nondec...

We propose the notion of nondecreasing Lyapunov functions which can be used to prove stability or other properties of the system in question. This notion is in particular useful in studying switched or hybrid systems. We illustrate the concept by a general construction of such a nondecreasing Lyapunov function for a class of planar hybrid systems. It is noted that this class encompasses switche...

In this paper, we proved some coincidence point results for f-nondecreasing self-mapping satisfying certain rational type contractions in the context of a metric space endowed with partial order. Moreover, consequences main result are given by involving integral space. Some numerical examples illustrated to support our results. As an application, have discussed existence unique solution equation.

In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation ut + (−∂ 2 x) α/2u+ uux = 0 with α ∈ (1, 2) is studied. It is shown that if the nondecreasing initial datum approaches the constant states u± (u− < u+) as x → ±∞, respectively, then the corresponding solution converges toward the rarefaction wave, i.e. the unique entropy sol...