12 citations · 15 across the 4 of their papers we have counts for
6 papers
An existence result for -Laplace equation with gradient nonlinearity in
Shilpa Gupta, Gaurav Dwivedi
We prove the existence of a weak solution to the problem \begin{equation*} \begin{split} -Δ_{p}u+V(x)|u|^{p-2}u & =f(u,|\nabla u|^{p-2}\nabla u), \ \ \ \\ u(x) & >0\ \ \forall x\in…
Kirchhoff type elliptic equations with double criticality in Musielak-Sobolev spaces
Shilpa Gupta, Gaurav Dwivedi
This paper aims to establish the existence of a weak solution for the non-local problem: \begin{equation*} \left\{\begin{array}{ll} -a\left(\int_Ω\mathcal{H}(x,|\nabla u|)dx \right…
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…
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…
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…
Picone's Identity for -biharmonic operator and Its Applications
Gaurav Dwivedi
In this article we prove the nonlinear analogue of Picone's identity for biharmonic operator. As an application of our result we show that the Morse index of the zero solution…