具快速增长非线性的定态Cahn-Hilliard方程解的遍历有限性

本文考虑具快速增长非线性的定态Ｃａｈｎ－Ｈｉｌｌｉａｒｄ方程的Ｎｅｕｍｍａｎ边值问题：－△（－△ｕ＋ｆ（ｕ））＝ｇ，１／｜Ω｜ｎｕｄｘ＝ａ证明了解的存在性和遍历有限性。

GENERIC FINITENESS OF THE SOLUTIONS FOR THE STABLE CAHN-HILLIARD EQUATION WITH FAST GROWING NONLINEARITY

Consider the Neumman boundary value problem of the stable Cahn-Hilliardequation -Δ(-Δu+f(u))=g. Under an additional condition(1-Ω)∫nudx=a, we prove thatfor every α∈R1 and g(g is given in some appropriate space),the problem has at least one solution.Moreover,for every α∈R1,the problem has at most finite number of solutions for almost all g.