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Multiple positive solutions to third-order three-point singular semipositone boundary value problem

Authors:

Huimin?Yu L?Haiyan Email author" target="_blank">Yansheng?Liu Email author

Institution:

(1) Department of Mathematics, Shandong Normal University, Jinan 250 014, People’s Republic of China

Abstract:

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order threepoint singular semipositone BVP:

$\left\{ \begin{gathered} x'(t) - \lambda f(t,x) = 0,t \in (0,1); \hfill \\ x(0) = x'(\eta ) = x'(1) = 0, \hfill \\ \end{gathered} \right.$

where 1/2 < η < 1, the non-linear term ƒ(t, x): (0, 1) × (0, + ∞) → (-∞, + ∞) is continuous and may be singular att = 0,t = 1, andx = 0, also may be negative for some values oft andx, λ is a positive parameter.

Keywords:

Singular semipositone boundary value problem cone positive solution fixed point theorem

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