辽宁石油化工大学学报 ›› 2012, Vol. 32 ›› Issue (3): 88-90.
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摘要: 在计算胶粒间双电层相互作用能时,需要计算胶粒间的电位分布,而两个胶粒间的电位分布满足Poisson-Boltzmann方程d2y/dt2=sinhy,这是一个二阶非线性常微分方程,无法求出其解析解。但是当y>>1时,sinhy≈ey/2,故求解Poisson-Boltzmann方程近似解问题转化为求d2y/dt2=ey/2解析解。因此,寻找常微分方程解解的问题是工程实际的需要。通过对二阶非线性常微分方程边值问题的研究,给出了一类二阶非线性常微分方程d2y/dt2=ey/a在等边值条件下的解析解表达式。
刘国志,刘倩囡. 一类非线性二阶常微分方程边值问题的解析解[J]. 辽宁石油化工大学学报, 2012, 32(3): 88-90.