arXiv subjects

J. Tyagi

Publications and source records attributed to J. Tyagi.

3 recordsLinked to original sources

arXiv2018

Sturm-Picone theorem for fractional nonlocal equations

In this paper, we establish a generalization of Sturm--Picone comparison theorem for a pair of fractional nonlocal equations: \begin{eqnarray*} \begin{gathered} (-div. (A_1(x)\nabla))^{s} u = C_{1}(x) u \,\,\,\mbox{in}\,\,Ω, u = 0 \,\,\,\,\mbox{on}\,\,\,\,\,\,\,\partial Ω, \end{gathered} \end{eqnarray*} and \begin{eqnarray*} \begin{gathered} (-div. (A_2(x)\nabla))^{s} v = C_{2}(x) v \,\,\,\mbox{in}\,\,Ω, v = 0 \,\,\,\,\mbox{on}\,\,\,\,\,\,\,\partial Ω, \end{gathered} \end{eqnarray*} where $Ω\subset \mathbb{R}^n$ is an open bounded subset with smooth boundary, $0<s<1,\,\,A_1,\,A_2$ are real symmetric and positive definite matrices on $Ω$ with continuous entries on $\overlineΩ$ and $C_{1}, C_{2}\in C(\overlineΩ).$

math.AP↗

arXiv2017

Lyapunov type inequality for extremal Pucci's equations

In this article, we establish Lyapunov type inequality for the following extremal Pucci's equation \begin{equation*} \left\{ \begin{aligned}{} \mathcal{M}^{+}_{λ,Λ}(D^{2}u)+a(x)u&=0~\text{in}~Ω,\\ u&=0~\text{on}~\partialΩ, \end{aligned} \right. \end{equation*} where $Ω$ is a smooth bounded domain in $\R^{N},~N\geq2$. This works generalize the well-known works on Lyapunov inequalities to fully nonlinear elliptic equations.

math.AP↗

arXiv2014

Some remarks on the qualitative questions for biharmonic equations

In this article, we obtain several interesting remarks on the qualitative questions such as stability criteria, Morse index, Picone's identity for biharmonic equations.

math.AP↗