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In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

In this paper, Numerical solution of Partial Diferential-Algebraic Equa- tions(PDAEs) is considered by Multivariate Padè Approximations. We applied these method to one example. First Partial Diferential-Algebraic Equation(PDAE) has been converted to power series by two-dimensional diferential transformation,Then the numerical solution of equation was put into Multivariate Padè series form. Thus we obtained numerical solution of Partial Diferential-Algebraic Equa- tion(PDAE). [ABSTRACT FROM AUTHOR]

This article claims to have established several existence theorems of positive solutions for nonlinear m-point boundary value problem for several dynamic equations on time scales. These equations include (φ(u&Delta))&nabla + α(t) f (t, u(t)) = 0, t ... (0,T), φ(uΔ(0)) = Σ i=1m-2 αiφ(uΔ(...i, u(T) = Σi=1m-2biu(...i, where φ : R &rar; R is an increasing homoemorphism and homomorphism and φ(0) = 0. It provides example calcalations using these equations.

The article reports on the complex analysis as catalyst. It states that topology has become part of the bedrock of modern mathematics and now permeates all branches of the discipline. The author also presents several examples from real analysis, group theory, abstract algebra, geometry, partial differential equations, and other subjects. He notes that these examples are given to show how a problem that began as a complex analysis problem could be resolved by techniques from another part of mathematics.

The article analyzes the boundary asymptotic behavior of solutions for weighted p(x)-Laplacian equations that take infinite value on a bounded domain. It was found that the boundary asymptotic of solutions of the Laplacian function is continuous and positive. The p(x)-Laplacian possesses more complicated inhomogeneous nonlinearities, thus, some special techniques are needed. Its main difficulty arises from the lack of compactness. The uniqueness and asymptotic behavior of solutions for problem is a nonnegative function which is allowed to vanish on the boundary.