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 $$-Î_{\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 consider the following problem: \begin{align*} -Î_{\mathbb{B}^N} u \, - \, λu = |u|^{p-1}u, \quad u \in H^{1}(\mathbb{B}^N), \end{align*} where , $Î…
Spike layered solutions for elliptic systems on Riemannian Manifolds
Anusree R Kannoth, Bhakti Bhusan Manna
In this article, we study the following Hamiltonian system: \begin{equation*} \begin{cases} \begin{aligned} &-\varepsilon^{2}Î_{g} u +u = |v|^{q-1}v, &-\varepsilon^{2}Î_{g} v +v…
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} -Îu - μ\frac{u}{|z|^2} = \frac{|u|^{q-2}u}{|z|^t}, \quad u \in D^{1,2} (\mathbb{R}^n)…