... Leray-Schauder degree.v If u x ψx is a critical p oint of mountain pass type of J,thenx is a critical point of mountain pass type of J.3. Proof of Theorem 1.3In this section, firstly, we obtain a ... boundedregions in E such thatS1∩K {0}, S2∩Kis the set of positive critical points of J,andS3∩Kis the set of negative critical points of J.Sofar,wehaveprovedthatdJ,S1, 0 1,dJ,S2, ... pagesdoi:10.1155/2011/172818 Research Article Existence of Positive, Negative, and Sign-ChangingSolutions to Discrete Boundary Value ProblemsBo Zheng,1Huafeng Xiao,1and Haiping Shi21School of Mathematics...