In this paper we study the linear Weingarten equation defined by fully non-linear PDEadivDu1+|Du|2+bdetD2u(1+|Du|2)2=ϕ(11+|Du|2) in a domain Ω⊂R2, where ϕ∈C1([−1,1]) and a,b∈R. We approach existence of radial solutions when Ω is disk small radius, giving an affirmative answer PDE elliptic type. hyperbolic case show that no solution exists, while parabolic find explicitly all solutions. prove un...

We investigate some equations involving the number of divisors d(n); sum σ(n); Euler's totient function ϕ(n); distinct prime factors ω(n); and all (counted with multiplicity) Ω(n). The first part deals equation f(xy) + f(xz) = f(yz). In second part, as an analogy to x2 y2 z2, we study f(x2) f(y2) f(z2) its generalization higher degrees more terms. use just elementary methods basic facts about a...