The purpose of this note is to show a generalization to Picone’s identity in a nonlinear framework. The classical Picone’s identity turns out to be a particular case of our result. We show, as an application of our results, ...

We establish the existence of nonnegative weak solutions to time fractional Keller�Segel system with Dirichlet boundary condition in a bounded domain with smooth boundary. Since the considered system has a cross?diffusion ...

In this note, we prove that theF-fundamental group schemeis a birational invariant for smooth projective varieties. We prove that theF-fundamental group scheme is naturally a quotient of the Nori fundamentalgroup scheme. ...

In this note, we establish Leighton's variational lemma for fractional Laplace equations. We use the classical techniques to establish this variational lemma. We also point out several questions concerning the zeros of the ...

In this note, we prove a stability theorem for a class of quasilinear elliptic equations -δp u = a(x)u-f(x,u) in Ω, u=0 on δΩ, where δp u= div(/∇uu/ p-2∇u) 2 ≤ p < p < ∞ ,Ω ⊂ &RdblN is an open, smooth and bounded subset. ...

In this paper, we carry out a fairly comprehensive study of two special classes of numerical semigroups, one generated by the sequence of partial sums of an arithmetic progression and the other one generated by a shifted ...

Let $ r_k(n)$ denote the number of representations of the positive integer $ n$ as the sum of $ k$ squares. In 1934, the Russian mathematician A. I. Popov stated, but did not rigorously prove, a beautiful series transformation ...

In this note, we discuss an eigenvalue problem involving Hardy's potential with homogeneous Dirichlet boundary condition in a smooth bounded domain. We show that the problem possesses a continuous family of eigenvalues.

In this article, we prove that the Faltings theta functions on moduli of parabolic bundles over a smooth projective curve can be used to give an explicit scheme-theoretic projective embedding.