Abstract: In this paper, we establish some sufficient conditions for the existence and nonexstence of positive solutions to a general class of higher-order nonlinear fractional differential equation. The results are established by converting the problem into an equivalent integral equation and applying Banach fixed point theorem, nonlinear differentiation of Leray-Schauder type and the fixed po...

A weighted graph is a graph provided with an edge-weighting function w from the edge set to nonnegative real numbers. Bondy and Fan [Annals of Discrete Math. 41 (1989), 53– 69] began the study on the existence of heavy cycles in weighted graphs. Though several results with Dirac-type degree condition can be generalized to Ore-type one in unweighted graphs, it is shown in [Bondy et al., Discuss....

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...

in this paper we consider the second order nonlinear neutral delay partial difference equation $delta_ndelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$under suitable conditions, by making use of the banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

Background : The teaching of differential equations is dominated by an excessively algebraised analytic tradition. For this reason, studies that contribute to conceptualising mathematical objects associated with the equation are important, particularly existence and uniqueness theorem. Objectives From its genesis, objective analyse nature knowledge, epistemology from practice. We give account v...

This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.