Solvability of a nonlinear fourth-order discrete problem at resonance
Solvability of a nonlinear fourth-order discrete problem at resonance
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DOI：
10.1016/j.amc.2010.01.112
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
Youji Xu;Chenghua Gao;Ruyun Ma
中科院分区：
文献类型：
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作者：
Youji Xu;Chenghua Gao;Ruyun Ma
设T是一个整数，T ≠ 5，T2={2，3，.，T}。本文考虑非线性离散边值问题，其中λ 1是相应的线性特征值问题的第一特征值，φ（·）是相应的特征函数; f：T2 ×R→R是连续的，且对某个0（t）φ（t）=0.我们证明了上述问题解的存在性。我们的方法是基于Krein-Rutman定理，连通性的参数化族的紧向量场的解决方案集。
Let T be an integer with T⩾5 and let T2={2,3,…,T}. We consider the nonlinear discrete boundary value problemwhere λ1is the first eigenvalue of the associated linear eigenvalue problem, φ(·) is the corresponding eigenfunction; f:T2×R→R is continuous andfor some 0⩽α<1 and A,B∈[0,∞);h¯:T2→R with ∑s=2Th¯(t)φ(t)=0. We show the existence of solutions of the above problem. Our approaches are based on the Krein–Rutman theorem, connectivity properties of solution sets of parameterized families of compact vector fields.