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math.AP2016
On the bifurcation for fractional Laplace equations
Gaurav Dwivedi, Jagmohan Tyagi, Ram Baran Verma
In this paper, we consider the bifurcation problem for fractional Laplace equation \begin{eqnarray*} \begin{array}{ll} (-Δ)^{s} u = λu + f(λ,\,x,\,u)& \mbox{in }Ω, u = 0 &\mbox{in…
math.AP2016
Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications
Gaurav Dwivedi, Jagmohan Tyagi
The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution to \b…
math.AP2016
Stability of positive solutions to biharmonic equations on Heisenberg group
Gaurav Dwivedi, Jagmohan Tyagi
In this note, we establish the existence of a positive solution and its stability to the following problem $$Δ_{\mathbb{H}^n}^2u=a(ξ)u-f(ξ,u)\text{ in }Ω, \,\,\, u|_{\partialΩ} = 0…