| Nonlinear partial differential equation usually arises in the natural science and engi-neering areas.Because they can well explain the important natural phenomenon,a large number of science researchers have paid attention to the problems for a long time.In this paper,we use the constraint variational method and the quantitative deformation lemma to study the existence of sign-changing solutions for the nonlinear Schr(?)dinger-Poisson system in R3.Our equation is of the following form:We say that(V,K)∈K if the following conditions hold:(H0)V(x)，K(x)>0 for all x∈R3 and K∈L∞(R3);(H1)if {An}(?)R3 is a sequence of Borel sets and for all n and some R>0,|An|≤R,then(H2)K/V∈L∞(R3);or(H3)there exists p∈(2,6)such thatAs for the function f,we assume f∈C1(R,R)and satisfies the following conditions:(f1)limt→0 f(t)/t=0,if(H2)hold;(f2)limt→0 f(t)/|t|p-1=A∈R,if(H3)hold;(f3)f has a "quasicritical growth"，namely,lim|t|→∞f(t)/t5=0;(f4)lim|t|→∞F(t)/t4=∞,where F(t)=∫0tf(s)ds;(f5)the map t→f(t)/|t|3 is nondecreasing on(-∞,0)and(0,∞)respectively.Our main result is the following theorem:Theorem Suppose that(V,K)∈K and f satisfies(f1)-(f5).Then the system(1.1)possesses at least one sign-changing solution. |
