Multiplicity Results for a Singular and Quasilinear Equation
نویسنده
چکیده
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 symmetric case (Ω = BR(0)), we prove by a shooting method the global multiplicity of solutions to (P ) in C(Ω̄) with 0 < δ, 1 < p and p− 1 < q.
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