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Positive solutions for some 1-dimensional boundary value problems of Laplace-type

Authors:

Zhanbing Bai Xiangqian Liang Weiming Li

Institution:

(1) Institute of Mathematics, Shandong University of Science and Technology, Qingdao, 266510, China

Abstract:

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type

$\left( {\phi (x'(t))} \right)^\prime + q(t)f(t,x(t),x'(t)) = 0, t \in (0,1),$

subject to the following boundary condition:

$a_1 \phi (x(0)) - a_2 \phi (x'(0)) = 0, a_3 \phi (x(1)) + a_4 \phi (x'(1)) = 0,$

where ϕ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly. Supported by the NNSF of China(10371006) and Tianyuan Youth Grant of China(10626033).

Keywords:

triple positive solution equation of Laplace-type boundary value problem fixed point theorem

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