二阶常微分方程组正解的存在性与多解性

doi:10.3976/j.issn.1002-4026.2015.06.018

SHANDONG SCIENCE ›› 2015, Vol. 28 ›› Issue (6): 116-120.doi: 10.3976/j.issn.1002-4026.2015.06.018

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Existence and multiplicity of positive solutions of secondorder ordinary differential equations

ZHOU Shilei,DONG Xue,DONG Xiaoyu

School of Mathematics and System Science,Shandong University of Science and Technology,Qingdao 266590,China

Received:2015-01-15 Published:2015-12-20 Online:2015-12-20

Abstract

Abstract: We address existence and multiplicity of positive solutions in boundary value problems of secondorder ordinary differential equations,u″(t)+λh1(t)f(u,v)=0,v″(t)+λh2(t)g(u,v)=0,u(0)=u(1)=v(0)=v(1)=0. With fixed point theorem and f(u,v) and g(u,v) satisfying a growth condition,we determine the scope of system parameter λ,which can ensure the system contains at least one or two positive solutions.

Key words: boundary value problems, positive solutions, multiple positive solutions, fixed point

CLC Number:

O175

ZHOU Shilei,DONG Xue,DONG Xiaoyu. Existence and multiplicity of positive solutions of secondorder ordinary differential equations[J].SHANDONG SCIENCE, 2015, 28(6): 116-120.

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Existence and multiplicity of positive solutions of secondorder ordinary differential equations

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