A continuous dependence of fixed points of ϕ\phi-contractive mappings in uniform spaces

summary:The main purpose of the present paper is to established conditions for a continuous dependence of fixed points of $\phi$-contractive mappings in uniform spaces. An application to nonlinear functional differential equations of neutral type have been made

On the existence and uniqueness of solutions for maximum equations

An existence-uniqueness result for the Cauchy problem for a system of ordinary differential equations with maximums is established

Oscillatory Solutions of Neutral Equations with Polynomial Nonlinearities

Existence uniqueness of an oscillatory solution for nonlinear neutral equations by fixed point method is proved

Lossless Transmission Lines Terminated by Linear and Nonlinear RLC-Loads

Here we consider lossless transmission lines terminated by a circuit consisting of linear and nonlinear RGCL-loads. First we overcome a difficulty caused by nonlinear boundary conditions utilizing Kirchhoff’s laws. The problem arising is to choose as many equations as are the unknown functions. Then we formulate the mixed problem for the hyperbolic system, reduce the mixed problem to an initial value problem on the boundary and obtain a neutral system with respect to new variables. Further on we prove an existence-uniqueness theorem for periodic solution in lossless case

A surjectivity result for nonlinear mappings on uniform spaces and applications

The main purpose of the present paper is to establish a surjectivity result for nonlinear continuous mappings on uniform spaces. Then one can prove that every surjective, continuous and expansive map of an uniform space onto itself has a unique fixed point. Moreover, such a map is a global homeomorphism of the uniform space onto itself. As a consequence of the main theorem a generalization of McCord's theorem to locally convex spaces is proved

A singular boundary value problem for neutral equations

Using some previous results of the author and Kirk-Schöneberg, theorems for the existence and uniqueness of an absolutely continuous solution of a singular boundary value problem for neutral equations have been proved

On the Black Body Oscillator Equation

[Angelov Vasil G.; Ангелов Васил Г.]The paper is concerned with the oscillator equation assigned to the black body. A new form of the Lorentz radiation term is derived. It corresponds to the original physical assumptions due to Dirac. This leads to a nonlinear functional differential equation of neutral type. By means of a fixed point theorem an existence result has been proved. As a consequence the ultra-violet catastrophe disappears