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Blow-up radial solutions for elliptic systems with monotonic non-linearities
Daniel Devine, Gurpreet Singh
We are concerned with the existence and boundary behaviour of positive radial solutions for the system \begin{equation*} \left\{ \begin{aligned} Δu&=g(|x|,v(x)) &&\quad\mbox{in}\ Ω…
A study of biharmonic equation involving nonlocal terms and critical Sobolev exponent
Gurpreet Singh
In this paper, we investigate the existence of ground state solutions and non-existence of non-trivial weak solution of biharmonic equation with some nonlocal terms and critical So…
Weighted Choquard equation perturbed with weighted nonlocal term
Gurpreet Singh
We investigate the following problem $$ -{\rm div}(v(x)|\nabla u|^{m-2}\nabla u)+V(x)|u|^{m-2}u= \Big(|x|^{-θ}*\frac{|u|^{b}}{|x|^α}\Big)\frac{|u|^{b-2}}{|x|^α}u+λ\Big(|x|^{-γ}*\fr…
Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms
Marius Ghergu, Paschalis Karageorgis, Gurpreet Singh
We investigate the existence and nonexistence of positive solutions for the quasilinear elliptic inequality $L_\mathcal{A} u= -{\rm div}[\mathcal{A}(x, u, \nabla u)]\geq (I_α\ast u…
Nonlocal Pertubations of Fractional Choquard Equation
Gurpreet Singh
We study the equation \begin{equation} (-Δ)^{s}u+V(x)u= (I_α*|u|^{p})|u|^{p-2}u+λ(I_β*|u|^{q})|u|^{q-2}u \quad\mbox{ in } \R^{N}, \end{equation} where for any $γ\…
Weak Solutions for Singular Quasilinear Elliptic Systems
Gurpreet Singh
We investigate the quasilinear elliptic system $-Δ_{m} u&=u^{-p}v^{-q}$, $u>0 \quad\mbox{ in } Ω$, $-Δ_{m} v&=u^{r}v^{-s}$, $v>0 \quad\mbox{ in }Ω$, $u=v=0 \quad\mbox{ on } \partia…