Existence and multiplicity of positive solutions for a singular problem associated to the p-Laplacian operator

Date

2004-11-16

Authors

Aranda, Carlos
Godoy, Tomas

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Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

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.

Description

Keywords

Singular problems, p-laplacian operator, Nonlinear eigenvalue problems

Citation

Aranda, C., & Godoy, T. (2004). Existence and multiplicity of positive solutions for a singular problem associated to the p-Laplacian operator. <i>Electronic Journal of Differential Equations, 2004</i>(132), pp. 1-15.

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Attribution 4.0 International

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