JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 88-95.doi: 10.6040/j.issn.1671-9352.0.2018.344

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Existence of positive solutions for a class of periodic boundary value problems of nonlinear second-order systems

MA Man-tang   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-06-05

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Abstract: We consider the existence of positive solutions for the periodic boundary value problems of nonlinear second-order systems{u″+A(t)u=ΛG(t)F(u), 01,…,un)T, A(t)=diag［a1(t),…,an(t)］, ai(t)can change the sign in ［0,1］ (i=1,…,n), G(t)=diag［g1(t),…,gn(t)］, F(u)=(f1(u),…, fn(u))T, Λ=diag(λ1,…,λn), λi is a positive parameter(i=1,…,n). Under the assumption that the nonlinear term F satisfies superlinear, sublinear and asymptotic growth condition, the existence of positive solutions of the problem are obtained by using the fixed-point theorem of cone expansion-compression. The conclusions in this paper generalize and improve the related results.

Key words: positive solutions, systems, cone, existence

CLC Number: 

  • O175.8
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