Jacques Giacomoni

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We investigate the following quasilinear and singular system,  −∆p1u = u1v1 in Ω −∆p2v = u2v2 in Ω u > 0, v > 0, u, v = 0 on ∂Ω, (P ) where Ω is an open bounded domain with smooth boundary, 1 < pi < ∞ and αi + βi < 0 for any i = 1, 2. We employ monotone methods in order to show the existence of a unique (positive) solution of problem (P ) in some(More)
In this paper, we are dealing with the following superlinear elliptic problem: (P) ( −∆u = λu+ h(x)up in RN , u ≥ 0, where h is a C2 function from RN to R changing sign such that Ω+ := {x ∈ RN | h(x) > 0}, Γ := {x ∈ RN | h(x) = 0} are bounded. For 1 < p < (n+ 2)/(n− 2) we prove the existence of global and connected branches of solutions of (P) in R−×H1(RN )(More)
In this paper, we investigate the following quasilinear elliptic and singular system (P): −∆pu = f1(x, u, v) in Ω ; u|∂Ω = 0, u > 0 in Ω, −∆qv = f2(x, u, v) in Ω ; v|∂Ω = 0, v > 0 in Ω, where Ω is a bounded domain with smooth boundary in R , 1 < p, q < ∞ and f1, f2 ∈ C 1 (Ω × R∗+ × R ∗ +) two positive functions. Under suitable conditions on f1 and f2, we(More)
In this paper, we investigate the following quasilinear and singular problem : { −∆pu = λ uδ + u q in Ω u|∂Ω = 0 , u > 0 in Ω (1) where Ω is an open bounded domain with smooth boundary, 1 < p, p− 1 < q and λ, δ > 0. We first prove that there exist weak solutions for λ > 0 small in W 1,p 0 (Ω)∩C(Ω̄) if and only if δ < 2+ 1 p−1 . Investigating the radial(More)
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