4 papers
A scalar field equation on hyperbolic space with indefinite sign nonlinearity
Debabrata Karmakar, Atanu Manna, Bhakti Bhusan Manna
In this article, we study threshold phenomena for the semilinear double-power elliptic equation $$-Δ_{\mathbb{B}^N} u - λu = |u|^{p-1}u - |u|^{q-1}u, \quad u \in H^1(\mathbb{B}^N),…
Existence and non-existence of nonradial solutions to an elliptic equation on hyperbolic space with critical and subcritical nonlinearities
Atanu Manna, Bhakti Bhusan Manna
In this article, we study the semi-linear elliptic problem: \begin{equation*} -Δ_{\mathbb{B}^N} u \, - \, λu = |u|^{p-1}u, \quad u \in H^{1}(\mathbb{B}^N), \end{equation*} where $N…
An improved Copson inequality
Bikram Das, Atanu Manna
In this paper, we prove that the discrete Copson inequality (E.T. Copson, \emph{Notes on a series of positive terms}, J. London Math. Soc., 2 (1927), 49-51) of one-dimension in gen…
Existence of a bi-radial sign-changing solution for Hardy-Sobolev-Mazya type equation
Atanu Manna, Bhakti Bhusan Manna
In this article, we study the following Hardy-Sobolev-Maz'ya type equation: \begin{equation} -Δu - μ\frac{u}{|z|^2} = \frac{|u|^{q-2}u}{|z|^t}, \quad u \in D^{1,2} (\mathbb{R}^n),…