In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existe...

We will prove existence and uniqueness theorems for solution of the boundary value problem x∆∆(t) = f(t, xσ(t)), x(a) = A, x(σ2(b)) = B for t in a measure chain T. In one of our results we use upper and lower solutions to prove the existence of a solution to this boundary value problem (BVP). We then use this result to show that if for each fixed t, f(t, x) is strictly increasing in x, then thi...

This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of a scalar backward stochastic differential equation (BSDE) whose generator grows (with respect both unknown variables y z) in super-linear way like |y||ln|y||?+|z||ln|z||? for some ??[0,1] ??0. Let k be maximum ?, ?+1/2 2?. For following four different ranges growth power parameter k: k=1/2, k?(1/...

in this paper, the goursat problem of a third order equation on cases of explicit solvability isinvestigated, with the help of the riemann function. some results and one theorem are given concerning theexistence and uniqueness for the solution of the suggested problem.

At the center of the theory of abelian p-groups are the classical theorems of Ulm, Zippin and Kaplansky, going back to the thirties, that classify countable p-groups by their Ulm invariants: the uniqueness theorem is referred to as Ulm's theorem, the existence theorem as Zippin's theorem. For each ordinal , the -th Ulm invariant of G can be de ned as the dimension fG( ) of the vector space (ove...

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

As new applications of Schrödinger type inequalities appearing in Jiang (J. Inequal. Appl. 2016:247, 2016), we first investigate the existence and uniqueness of a Schrödingerean equilibrium. Next we propose a tritrophic Hastings-Powell model with two different Schrödingerean time delays. Finally, the stability and direction of the Schrödingerean Hopf bifurcation are also investigated by using t...