二阶共振离散问题解的多重性

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二阶共振离散问题解的多重性

应用基础研究 | 更新时间：2026-09-14

- 二阶共振离散问题解的多重性
- Multiplicity of Solutions for Second Order Discrete Problems with Resonance
- 中北大学学报（自然科学版） 2012年33卷第4期页码：369-371
- 作者机构：
  
  太原理工大学数学学院
- 作者简介：
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- 纸质出版：2012
- 稿件说明：
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覃舟. 二阶共振离散问题解的多重性[J]. 中北大学学报（自然科学版）, 2012,33(4):369-371.

覃舟. Multiplicity of Solutions for Second Order Discrete Problems with Resonance[J]. 2012, 33(4): 369-371.
覃舟. 二阶共振离散问题解的多重性[J]. 中北大学学报（自然科学版）, 2012,33(4):369-371. DOI：

覃舟. Multiplicity of Solutions for Second Order Discrete Problems with Resonance[J]. 2012, 33(4): 369-371. DOI：

摘要

利用山路引理讨论了带共振的二阶差分方程边值问题解的多重性.把方程的解等价于泛函的临界点

且在一定的假设条件下采用函数的截断技术

结合非线性泛函分析中的变分方法

特别是临界群与Morse理论

分4步最终证明了方程至少存在两个解.

Abstract

Multiplicity of solutions of boundary value problems of second order discrete function with resonance was discussed by means of mountain pass lemma.The solution of the function is equivalent to the critical point of the functional.For the problems under certain conditions

four steps were taken in proving the existence of at least tow solutions by using the truncation technique

and variational method of nonlinear functional analysis

critical groups and the Morse theory.

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references

Hatsunaga H,Hara T,Sakata S.Global attractivity for a nonlinear difference equation with variable delay[J].Computer Math.Applica,2001,41:543-551.

Cabada A,Iannizzotto A,Tersian S.Multiple solutions for discrete boundary value problems[J].J.Math.Anal.Appl.,2009,356:418-428.

Zhu Benshi,Yu Jianshe.Multiple positive solutions for resonant difference equations[J].Mathematics&Computer Modelling,2009,49:1928-1936.

Zou Wenming.Multiple solutions for elliptic equations with resonance[J].Nonlinear Analysis,2002,48:363-376.

Liu Shibo.Nontrivial solutions for elliptic resonant problems[J].Nonlinear Analysis,2009,70:1965-1974.

Su Jiabao,Tang Chunlei.Multiplicity results for semilinear elliptic equations with resonance at higher eigenvalues[J].Nonlinear Analysis,2001,44:311-321.

Bai Dingyong,Xu Yuantong.Nontrivial solutions of boundary value problems of second-order difference equations[J].J.Math.Anal.Appl.,2007,326:297-302.

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