20 citations · 53 across the 46 of their papers we have counts for
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Biharmonic equation with singular nonlinearity
J. Giacomoni, S. Prashanth, G. Warnault
We consider the following problem: \begin{eqnarray*} ( P)\qquad \displaystyle\left\{\begin{array} {ll} & Δ^2 u = K(x)u^{-α} \quad \mbox{ in }\,Ω, \\ &u> 0\quad \mbox{ in }\,Ω, \;\;…
Critical growth fractional systems with exponential nonlinearity
Jacques Giacomoni, Pawan Kumar Mishra, Konijeti Sreenadh
We study the existence of positive solutions for the system of fractional elliptic equations of the type, \begin{equation*} \begin{array}{rl} (-Δ)^{\frac{1}{2}} u &=\frac{p}{p+q}λf…
Critical exponent for half-Laplacian in the whole space
Jacques Giacomoni, Pawan Mishra, Konijeti Sreenadh
We study the existence of {weak} solutions for fractional elliptic equations of the type, \begin{equation*} (-Δ)^{\frac{1}{2}} u+ V(x) u= h(u), u> 0 \;\textrm{in} \;\mathbb R, \end…
Existence and regularity of weak solutions for singular elliptic equations
Brahim Bougherara, Jacques Giacomoni, Jesus Hernandez
In the present paper we investigate the following semilinear singular elliptic problem: \begin{equation*} (\rm P)\qquad \left \{\begin{array}{l} -Δu = \dfrac{p(x)}{u^α}\quad \text{…
Quasilinear parabolic problem with -Laplacian: existence, uniqueness of weak solutions and stabilization
Jacques Giacomoni, Sweta Tiwari, Guillaume Warnault
We discuss the existence and uniqueness of the weak solution of the following quasilinear parabolic equation in ; on $(0,T)\times\pa…
Uniqueness of positive solutions of a -Laplace equation in a ball in with exponential nonlinearity
Adimurthi, Karthik A, Jacques Giacomoni
Let and be a bounded domain. Then by Trudinger-Moser embedding, is embedded in an Orlicz space consisting of exponential functions…