In this paper, we deal with the biharmonic heat equation gradient non-linearity. Under suitable condition of initial datum, show that global unique existence mild solution. The main technique in paper is to use Banach?s fixed point theorem combination Lp-Lq evaluation operator.

This work studies the existence and p-th moment asymptotic stability of mild solution some neutral fractional stochastic integro-differential equations involving non-instantaneous impulses Poisson jumps. Sufficient conditions proving solutions are obtained utilizing analysis, resolvent operator Krasnoselskii-Schaefer type fixed point theorem.

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

The aim of this work is to model a jet diffusion flame, to show the corresponding proof of existence of solutions, and to present numerical results. The model is based on the flamelet equations for the chemistry and on the mixture fraction for the flow. Numerical tests are carried out for Sandia Flame D and the results are found to compare well with available data found in the literature.

We prove a general finite-dimensional reduction theorem for critical equations of scalar curvature type. Solutions of these equations are constructed as a sum of peaks. The use of this theorem reduces the proof of existence of multi-peak solutions to some test-functions estimates and to the analysis of the interactions of peaks.

This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining mild solution, we establish fundamental unique existence, limited smoothing property and long-time asymptotic behavior which mostly inherit those single equation. Owing to coupling effect, also obtain uniqueness an inverse on determining all fractional orde...

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

We show lower bounds on the number of sample points and on the number of coin tosses used by general sampling algorithms for estimating the average value of functions over a large domain. The bounds depend on the desired precision and on the error probability of the estimate. Our lower bounds match upper bounds established by known algorithms, up to a mul-tiplicative constant. Furthermore, we g...

This paper presents an application of voting geometry to individual decision making. We demonstrate that a number of decision anomalies can arise as a natural consequence of the aggregation of preferences of different neural systems. We present a proof of existence of a set of voting procedures that can account for the attraction effect, the similarity effect and the compromise effect, and prov...