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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…
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),…
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}Δ_{g} u +u = |v|^{q-1}v, &-\varepsilon^{2}Δ_{g} v +v =…
Concentration results for solutions of a singularly perturbed elliptic system with variable coefficients
Alok kumar Sahoo, Bhakti Bhusan Manna
In this article we shall study the following elliptic system with coefficients: \begin{equation}\notag \left\{\begin{aligned} -ε^2Δu +c(x)u=b(x)|v|^{q-1}v, &\text{ and } -ε^2Δv +c(…
Boundary-layers for a Neumann problem at higher critical exponents
Bhakti B. Manna, Angela Pistoia
We consider the Neumann problem w…
On a problem of resonance with exponential non linearity
B. B. Manna, P. N. Srikanth
We have considered the following semi linear elliptic problem on the unit disk in with the Dirichlet boundary condition and satisfying the followin…
On the solutions of a singular elliptic equation concentrating on a circle
B. B. Manna, P. N. Srikanth
Let be an annulus. Consider the following singularly perturbed elliptic problem on \begin{equation} \begin{array}{lll} -\eps^2{\De u} + |x…
On the solutions of a singular elliptic equation concentrating on two orthogonal spheres
B. B. Manna, P. N. Srikanth
Let be an annulus. Consider the following singularly perturbed elliptic problem on \begin{equation} \begin{array}{lll} -\eps^2{\De u} + |x|^…