Positive solutions for a system of nonlinear boundary-value problems on time scales

Electronic Journal of Differential Equations

关键词: Dynamic equations;    eigenvalue intervals;    positive solution;    cone;   

DOI  :  

来源: DOAJ

【 摘 要 】

We determine the values of a parameter $lambda$ for which thereexist positive solutions to the system of dynamic equations$$displaylines{u^{Delta Delta}(t)+lambda p(t)f(v(sigma(t)))=0,quadtin[a, b]_mathbb{T}, crv^{Delta Delta}(t)+lambda q(t)g(u(sigma(t)))=0,quad tin[a, b]_mathbb{T},}$$with the boundary conditions,$alpha u(a)-eta u^{Delta}(a)=0$,$gamma u(sigma^2(b))+delta u^{Delta}(sigma(b))=0$,$alpha v(a)-eta v^{Delta}(a)=0$,$gamma v(sigma^2(b))+delta v^{Delta}(sigma(b))=0$, where$mathbb{T}$ is a time scale. To this end we apply a Guo-Krasnosel'skiifixed point theorem.

【 授权许可】

Unknown