TY - JOUR

T1 - Positive solutions of nonlinear three-point boundary-value problems

AU - Ma, Ruyun

AU - Wang, Haiyan

N1 - Funding Information:
* Corresponding author. E-mail address: mary@nwnu.edu.cn (R. Ma). 1 Supported by the NSFC (10271095), GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major Project of Science and Technology of Chinese Education Ministry.

PY - 2003/5/1

Y1 - 2003/5/1

N2 - Let a ∈ C[0, 1], b ∈ C([0, 1], (-∞, 0]). Let φ1 (t) be the unique solution of the linear boundary value problem u″(t) + a(t)u′(t) + b(t)u(t) = 0, t ∈ (0,1), u(0) = 0, u(1) = 1. We study the existence of positive solutions to the nonlinear boundary-value problem u″(t) + a(t)u′(t) + b(t)u(t) + h(t)f(u) = 0, t ∈ (0,1), u(0) = 0, αu(η) = u(1). where 0 < η < 1 and 0 < αφ1(η) < 1 are given, h ∈ C([0, 1], [0, ∞)) satisfying that there exists x0 ∈ [0, 1] such that h(x0) > 0, and f ∈ C([0, ∞), [0, ∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.

AB - Let a ∈ C[0, 1], b ∈ C([0, 1], (-∞, 0]). Let φ1 (t) be the unique solution of the linear boundary value problem u″(t) + a(t)u′(t) + b(t)u(t) = 0, t ∈ (0,1), u(0) = 0, u(1) = 1. We study the existence of positive solutions to the nonlinear boundary-value problem u″(t) + a(t)u′(t) + b(t)u(t) + h(t)f(u) = 0, t ∈ (0,1), u(0) = 0, αu(η) = u(1). where 0 < η < 1 and 0 < αφ1(η) < 1 are given, h ∈ C([0, 1], [0, ∞)) satisfying that there exists x0 ∈ [0, 1] such that h(x0) > 0, and f ∈ C([0, ∞), [0, ∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.

KW - Cone

KW - Fixed point

KW - Positive solution

KW - Second-order multi-point BVP

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U2 - 10.1016/S0022-247X(02)00661-3

DO - 10.1016/S0022-247X(02)00661-3

M3 - Article

AN - SCOPUS:0037658906

VL - 279

SP - 216

EP - 227

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -