Abstract
We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique.
Highlights
We study the existence and multiplicity of positive periodic solutions of the following singular nonlinear third-order periodic boundary value problem: u ρ3u f t, u, 0 ≤ t ≤ 2π, 1.1 u i 0 u i 2π, i 0, 1, 2. √ Here ρ ∈ 0, 1/ 3 is a positive constant and f t, u is continuous in t, u and 2π- is periodic in t
We are mainly interested in the case that f t, u may be singular at u 0 and satisfies the following semipositone condition: G1 There exists a constant L > 0 such that F t, u f t, u L ≥ 0 for all t, u ∈ 0, 2π × 0, ∞
Boundary Value Problems of multiple positive solutions was obtained by using the fixed-point index theory
Summary
We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique. Copyright q 2008 Yigang Sun. Copyright q 2008 Yigang Sun
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