
Existence of positive solutions for a class of periodic boundary value problems of nonlinear secondorder systems
 MA Mantang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(6):
8895.
doi:10.6040/j.issn.16719352.0.2018.344

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We consider the existence of positive solutions for the periodic boundary value problems of nonlinear secondorder systems{u″+A(t)u=ΛG(t)F(u), 0<t<1,u(0)=u(1), u'(0)=u'(1)where u=(u_{1},…,u_{n})^{}T, A(t)=diag［a_{1}(t),…,a_{n}(t)］, a_{i}(t)can change the sign in ［0,1］ (i=1,…,n), G(t)=diag［g_{1}(t),…,g_{n}(t)］, F(u)=(f_{1}(u),…, f_{n}(u))^{}T, Λ=diag(λ_{1},…,λ_{n}), λ_{i} 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 fixedpoint theorem of cone expansioncompression. The conclusions in this paper generalize and improve the related results.