在第一特征值处共振的超线性Neumann问题的可解性OA
Solvability of a superlinear Neumann problem at resonance in the first eigenvalue
研究一类超线性二阶离散Neumann边值问题{-Δ2u(t-1)=(u+(t))p+f(t),t ∈[1,T]Z,Δu(0)=Δu(T)=0,解的存在性,其中T≥2为整数,p>1,函数f 满足T∑t=1f(t)<0.利用拓扑度理论,证明了问题至少存在一个解.此外,将相关方法推广至具有类似非线性结构的二阶离散方程组.
The existence of solutions for a class of superlinear second-order discrete Neumann boundary value problems of the form{-Δ2u(t-1)=(u+(t))p+f(t),t ∈[1,T]Z,Δu(0)=Δu(T)=0,where T≥2 is an integer,p>1,and f satisfies the condition T∑t=1 f(t)<0,is investigated.Based on the t=1 T topological degree theory,we show that the problem possesses at least one solution.Additionally,we extend our analysis to systems of second-order discrete equations with similar nonlinearities.
张亚莉
甘肃政法大学人工智能学院,甘肃 兰州 730070
数理科学
离散方程共振超线性拓扑度
discrete equationsresonancesuperlinearitytopological degree
《中山大学学报（自然科学版）（中英文）》 2026 (5)
168-176,9
Supported by Scientific Research and Innovation Projects of Gansu University of Political Science and Law(299/6360677)
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