Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
نویسندگان
چکیده
منابع مشابه
Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problem
We study the existence and multiplicity of positive solutions for a class of nth-order singular nonlocal boundary value problems u(n)(t) + a(t) f (t,u) = 0, t ∈ (0,1), u(0) = 0, u′(0) = 0, . . . ,u(n−2)(0) = 0, αu(η) = u(1), where 0 < η < 1, 0 < αηn−1 < 1. The singularity may appear at t = 0 and/or t = 1. The Krasnosel’skii-Guo theorem on cone expansion and compression is used in this study. Th...
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Intervals of the parameter λ are determined for which there exist positive solutions for the system of nonlinear differential equations, u(n) + λa(t)f(v) = 0, v(n)+λb(t)g(u) = 0, for 0 < t < 1, and satisfying three-point nonlocal boundary conditions, u(0) = 0, u(0) = 0, . . . , u(n−2)(0) = 0, u(1) = αu(η), v(0) = 0, v(0) = 0, . . . , v(n−2)(0) = 0, v(1) = αv(η). A Guo-Krasnosel’skii fixed point...
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Under various weaker conditions, we establish various results on the existence and nonexistence of positive solutions for singular third-order nonhomogeneous boundary value problems with nonlocal boundary conditions. The arguments are based upon the fixed point theorem of cone expansion and compression. Finally, we give two examples to demonstrate our results. Key–Words: Positive solutions, Fix...
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We discuss the existence of positive solutions of a nonlinear nth order boundary value problem u(n) + a(t) f (u) = 0, t ∈ (0, 1) u(0) = 0, u′(0) = 0, . . . , u(n−2)(0) = 0, αu(η) = u(1), where 0 < η < 1, 0 < αηn−1 < 1. In particular, we establish the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones due to Krasnoselk...
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We consider the existence of countably many positive solutions for nonlinear nth-order three-point boundary value problem u n t a t f u t 0, t ∈ 0, 1 , u 0 αu η , u′ 0 · · · u n−2 0 0, u 1 βu η , where n ≥ 2, α ≥ 0, β ≥ 0, 0 < η < 1, α β − α ηn−1 < 1, a t ∈ L 0, 1 for some p ≥ 1 and has countably many singularities in 0, 1/2 . The associated Green’s function for the nth-order three-point bounda...
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ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2007
ISSN: 1687-2762
DOI: 10.1155/2007/74517