О РАСПРЕДЕЛЕНИИ ЗНАЧЕНИЙ НЕПОЛНЫХ СУММ ГАУССА

The theorems on the distribution of absolute values incomplete Gauss sums are proved. Asymptotic formulas of the fractional moments of incomplete Gauss sums are proved.Доказана теорема о распределении значений неполных сумм Гаусса. Получены асимптотические формулы для дробных моментов этих сумм

Solvability of the boundary-value problem for a partial quasilinear differential equation of the fourth order

We use a topological method implying the reduction of the initial problem to solving an operational equation in a Hilbert space and consequent calculation of the rotation of the corresponding vector field. We show that in a sphere of a sufficiently large radius the problem has at least one generalized solution. © Allerton Press, Inc., 2010

Solvability of the boundary-value problem for a partial quasilinear differential equation of the fourth order

We use a topological method implying the reduction of the initial problem to solving an operational equation in a Hilbert space and consequent calculation of the rotation of the corresponding vector field. We show that in a sphere of a sufficiently large radius the problem has at least one generalized solution. © Allerton Press, Inc., 2010

Solvability of the boundary-value problem for a partial quasilinear differential equation of the fourth order

We use a topological method implying the reduction of the initial problem to solving an operational equation in a Hilbert space and consequent calculation of the rotation of the corresponding vector field. We show that in a sphere of a sufficiently large radius the problem has at least one generalized solution. © Allerton Press, Inc., 2010