吉林大学学报（理学版）2016，Vol.54Issue(5)：945-951,7.DOI:10.13413/j.cnki.jdxblxb.2016.05.04
带非线性边界条件的二阶差分方程正解的全局结构
Global Structure of Positive Solutions for Second-Order Difference Equations with Nonlinear Boundary Conditions
摘要
Abstract
By using bifurcation theory,the author investigated the global structure of positive solutions for the following second-order nonlinear discrete boundary value problem{-Δ[p (k - 1)Δu(k - 1)]+q(k)u(k)=λa (k)f (u(k)), k ∈ [1,N ]Z , g 1 (λ,u(0),Δu(0))=0, g 2 (λ,u(N + 1),Δu(N ))=0 , and obtained the optimal sufficient conditions for the existence of the positive solution of the problem. whereλ>0 is parameter,[1,N ]Z = {1,2,…N },p :[0,N + 1 ]Z → ℝ+ ,q ,a :[1,N ]Z → ℝ+ and a(k)>0,∀k ∈[1,N ]Z ,g 1 ∈C (ℝ+ × ℝ+ × ℝ+ ,ℝ+ ),g 2 ∈C (ℝ+ × ℝ+ × (- ∞,0 ],ℝ+ ), f ∈C(ℝ+ ,ℝ+ ).关键词
差分方程/非线性边界条件/正解/Dancer分歧理论Key words
difference equation/nonlinear boundary condition/positive solution/Dancer’s bifurcation theory分类
数理科学引用本文复制引用
苏艳..带非线性边界条件的二阶差分方程正解的全局结构[J].吉林大学学报（理学版）,2016,54(5):945-951,7.基金项目
国家自然科学基金(批准号:11361054) （批准号:11361054）
