共查询到20条相似文献,搜索用时 31 毫秒
1.
Intervals of the parameters λ and μ are determined for which there exist positive solutions to the system of dynamic equations $$ \begin{array}{lll} && (-1)^nu^{\Delta^{2n}}(t)+\lambda p(t)f(v(\sigma(t)))=0,\quad t\in[a, b], \\ &&(-1)^n v^{\Delta^{2n}}(t)+\mu q(t)g(u(\sigma(t)))=0, \quad t\in[a, b], \end{array} $$ satisfying the Sturm–Liouville boundary conditions $$ \begin{array}{lll} &&\alpha_{i+1} u^{\Delta^{2i}}(a)-\beta_{i+1} u^{\Delta^{2i+1}}(a)=0,\;\gamma_{i+1} u^{\Delta^{2i}}(\sigma(b))+\delta_{i+1} u^{\Delta^{2i+1}}(\sigma(b))=0,\\ &&\alpha_{i+1} v^{\Delta^{2i}}(a)-\beta_{i+1} v^{\Delta^{2i+1}}(a)=0,\; \gamma_{i+1} v^{\Delta^{2i}}(\sigma(b))+\delta_{i+1} v^{\Delta^{2i+1}}(\sigma(b))=0, \end{array} $$ for 0?≤?i?≤?n???1. To this end we apply a Guo–Krasnosel’skii fixed point theorem. 相似文献
2.
In this paper, we are concerned with the existence criteria for positive solutions of the following nonlinear arbitrary order
fractional differential equations with deviating argument
$\left \{{l@{\quad}l}D_{0^+}^{\alpha}u(t)+h(t)f(u(\theta(t)))=0, & t\in ( 0,1 ),\ n-1<\alpha\leq n,\\[3pt]u^{(i)}(0)=0, & i=0,1,2,\ldots,n-2,\\[3pt][D_{0^+}^{\beta} u(t)]_{t=1}=0, & 1\leq\beta\leq n-2, \right .$\left \{\begin{array}{l@{\quad}l}D_{0^+}^{\alpha}u(t)+h(t)f(u(\theta(t)))=0, & t\in ( 0,1 ),\ n-1<\alpha\leq n,\\[3pt]u^{(i)}(0)=0, & i=0,1,2,\ldots,n-2,\\[3pt][D_{0^+}^{\beta} u(t)]_{t=1}=0, & 1\leq\beta\leq n-2,\end{array} \right . 相似文献
3.
Nguyen Thanh Chung 《Acta Appl Math》2010,110(1):47-56
This paper deals with the existence of weak solutions to a class of degenerate and singular elliptic systems in ℝ
N
, N
≧2 of the form
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