In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction‐diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.

中文翻译：

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具有Dirac相互作用的双幂反应扩散方程平衡解的稳定性

本文提供了关于一维非线性局部反应扩散方程族的平衡解的不稳定性的信息。更精确地，计算出平衡解的显式公式，并通过解析扰动理论，分析了与稳定性问题相关的线性算子的正特征值的确切数目。此外，还讨论了爆破方程解的充分条件。