Existence and multiplicity of positive solutions for a singular problem associated to the p-Laplacian operator
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Consider the problem
-Δpu = g(u) + λh(u) in Ω
with u = 0 on the boundary, where λ ∈ (0, ∞), Ω is a strictly convex bounded and C2 domain in ℝN with N ≥ 2, and 1 p ≤ 2. Under suitable assumptions on g and h that allow a singularity of g at the origin, we show that for λ positive and small enough the above problem has at least two positive solutions in C(Ω)∩(C1(Ω) and that λ = 0 is a bifurcation point from infinity. The existence of positive solutions for problems of the form -Δpu = K(x)g(u) + λh(u) + ƒ(x) in Ω, u = 0 on ∂Ω is also studied.
CitationAranda, C., & Godoy, T. (2004). Existence and multiplicity of positive solutions for a singular problem associated to the p-Laplacian operator. Electronic Journal of Differential Equations, 2004(132), pp. 1-15.
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