Solving functional equations at higher types: some examples and some theorems.

Stability theorems for some functional differential equations

Some Incidence Theorems and Integrable Discrete Equations

Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of Pascal theorem due to Möbius give rise to double cross-ratio equation and Hietarinta equation. The construction corresponding to the double cross-ratio equation is a reduction to a conic section of some planar configuration (203154). This configuration provides a correct definitio...

Some Theorems and Conjectures in Diophantine Equations

The theory of diophantine equations may be regarded as the natural continuation of algebraic geometry proper: Having once obtained a general theory of algebraic equations in several variables over essentially arbitrary ground fields (or rings), one tries to get statements depending on the special arithmetic structure of the coefficient domain. By definition, this becomes diophantine analysis. W...

Some Logarithmic Functional Equations

The functional equation f(y − x) − g(xy) = h (1/x− 1/y) is solved for general solution. The result is then applied to show that the three functional equations f(xy) = f(x)+f(y), f(y−x)−f(xy) = f(1/x−1/y) and f(y−x)−f(x)−f(y) = f(1/x−1/y) are equivalent. Finally, twice differentiable solution functions of the functional equation f(y − x) − g1(x) − g2(y) = h (1/x− 1/y) are determined.

Some Solvability Theorems for Nonlinear Equations

Let E be a locally convex space and f : E → E a mapping. We say that the equation f(x) = 0 is almost solvable on A ⊂ E if 0 ∈ f(A). In this paper some results about the solvability and almost solvability are given. Our results are based on some classical fixed point theorems and on some geometrical conditions.