一类带跳跃非线性项的边值问题的非平凡解的存在性

Existence of Nontrivial Solutions for a Class of Boundary Value Problem with Jumping Nonlinearity

设Ω为 R^n(n≥1)的有界光滑区域,g∈C(R,R).本文得到边值问题—△u=g(u)在Ω内,u=0在 aΩ上在 g 满足适当跳跃性和局部光滑性条件时存在两个非平凡解.

Let Ω be a bounded smooth domain in R^n(n≥1),g∈C(R,R).This paperhas proved the boundary value problem—△u=g(u) inΩ,u=O on (?)Ωhas two nontrivial solutions whenever g satisfies suitable jumping and locally smoothconditions.