权值不定的二阶离散周期边值问题正解的全局结构

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-10-01 DOI:10.1216/rmj.2023.53.1525

Ruyun Ma, Yali Zhang

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引用次数: 0

摘要

给出了二阶周期边值问题{−Δ2u(t−1)=λa(t)g(u(t))的正解的整体结构，其中，t∈∈n = t,u(0)=u(t)，u(1)=u(t +1)，其中，n ={1,2，…，t}， t≥3是整数，λ>0是参数，g:[0，∞)→[0，∞)是连续函数，g(0)=0, a: n = n→t是变号函数。根据g在0和∞附近的行为，我们得到了λ∈(0，λ0)存在0λ1且无解。我们的主要结果的证明是基于分岔技术。

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GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR SECOND ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEM WITH INDEFINITE WEIGHT

We show the global structure of positive solutions for second order periodic boundary value problem { −Δ2u(t−1)=λa(t)g(u(t)), t∈ℕ1T,u(0)=u(T), u(1)=u(T+1), where ℕ1T={1,2,…,T},T≥3 is an integer, λ>0 is a parameter, g:[0,∞)→[0,∞) is a continuous function with g(0)=0 and a:ℕ1T→ℝ is sign-changing. Depending on the behavior of g near 0 and ∞, we obtain that there exist 0<λ0≤λ1 such that above problem has at least two positive solutions for λ>λ1 and no solution for λ∈(0,λ0). The proof of our main results is based upon bifurcation technique.

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.