Given a negative plurisubharmonic function $\phi $ in a bounded pseudoconvex domain of $\mathbb C^n$, we introduce and study its <em>residual function</em> $g_\phi $ determined by the asymptotic behavior of $\phi $ near its singularity points, both inside

We apply a Fourier–Legendre-based technique recently introduced by Campbell et al.&nbsp;[J.&nbsp;Math.&nbsp;Anal.&nbsp;Appl. 479 (2019), 90–121], to prove new rational double hypergeometric series formulas for expressions involving $ {1}/{\pi ^2}$, especi

We study the existence of solutions for the following quasilinear Schrödinger equation: $$ -\Delta u-\Delta (u^2)u=|u|^{2\cdot 2^*-2}u+g(u), \quad x\in \mathbb {R}^N, $$ where $N\geq 3$ and $g$ satisfies very weak growth conditions. The method is to analy

We extend the study of jumping numbers of multiplier ideals due to Ein–Lazarsfeld–Smith–Varolin from the algebraic case to the case of general plurisubharmonic functions. While many properties established by Ein–Lazarsfeld–Smith–Varolin are shown to gener

We prove a regularity criterion for local strong solutions of the Stokes-MHD equations in terms of the velocity field in Besov space $ \dot {B}_{\infty ,\infty }^{0}$.

We prove the existence and uniqueness of a periodic solution to neutral function partial differential equations with infinite delay of the form $$ \frac {\partial Fu_t}{\partial t}= A(t)Fu_t +g(t,u_t)\quad \mbox {for } t \gt 0,\quad u(t)=\phi (t)\quad \hb

We obtain some eigenvalue comparison theorems for Finsler manifolds with integral Ricci curvature bound.

We discuss the convergence/divergence problem for formal holomorphic mappings sending real-analytic CR submanifolds into real-analytic sets both lying in complex Euclidean spaces of arbitrary dimension. In particular, we survey the recent developments on

We first prove that a $(k,\mu )$-contact manifold of dimension $2n+1$ with divergence free Cotton tensor is flat in dimension $ 3 $, and in higher dimensions, locally isometric to $S^n(4)\times E^{n+1}$. Finally, we show that a Bach flat non-Sasakian $(k,

The main result of the present paper is that a function defined on a union of lines CE through the origin in C-n with directional vectors in E subset of C-n and holomorphic of fixed finite order and finite type along each of these lines can be extended to an entire function of the same order and finite type provided that CE is not pluripolar and all directional derivatives along the lines satisfy a necessary compatibility condition at the origin. We are able to estimate the indicator function of the extension in terms of Siciak's weighted homogeneous extremal function, where the weight is a function of the type of the given function on each given line. As an application we prove a generalization of Helgason's support theorem by showing how the support of a continuous function with rapid decrease at infinity can be located from partial information about the support of its Radon transform.