Comparison theorems for non-linear vector differential equations

Differentiability Theorems for Non - Linear Elliptic Equations

^ C O and Z)0(x) stand for ——^ ^ " ^ T » (bx ) . . . (o* ) y and Dz stands for all the derivatives Dz for i = \, . . . , N and 0 < |a| < mt (of course if |a | = 0 , Dz = z). Equations of the form (1 ) were discussed in my paper "Partial regularity theorems for elliptic systems" which appeared in the January 1968 issue of the Journal of Mathematics and Mechanics [17] where it was assumed that th...

Oscillation theorems for systems of linear differential equations

Solutions for some non-linear fractional differential equations with boundary value problems

In recent years, X.J.Xu [1] has been proved some results on mixed monotone operators.  Following the paper of X.J.Xu, we study the existence and uniqueness of the positive solutions for non-linear differential equations with boundary value problems. 

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Comparison Theorems for Half-linear Differential Equations of the Fourth Order

An identity of the Picone type for fourth-order half-linear ordinary differential operators of the form lα[x] ≡ (pφ(x′′))′′ − (rφ(x′))′ + qφ(x) and Lα[y] ≡ (Pφ(y′′))′′ − (Rφ(y′))′ +Qφ(y). where φ(u) := |u|α−1u, α > 0, u ∈ R, and p, q, r, P,Q and R are continuous functions on a given interval I is derived and then Sturmian comparison theory for the corresponding fourth-order equations lα[x] = 0 ...