特征值乘数为 2 的情况下存在的必要条件和充分条件

Pub Date : 2024-01-24 DOI:10.58997/ejde.2024.09

Philip Korman

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引用次数: 0

摘要

我们为一类线性部分在特征值为 2 时处于共振的半线性迪里夏特问题的解的存在性建立了必要和充分条件。应用这一结果给出了相应半线性热方程所有解的非约束性条件。更多信息请参见 https://ejde.math.txstate.edu/Volumes/2024/09/abstr.html

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Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two

We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation. For more information see https://ejde.math.txstate.edu/Volumes/2024/09/abstr.html

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