考虑了非线性项是变号的m-点奇异p-Laplacian动力方程(p(u~△(t)))~▽+ q(t)f(t,u(t))=0,t∈(0,T)_T,u(0)=0,_p(u~△(T))=sum from i=1 to m-2_i(u~△(ξ_i)),其中_p(s)= |s|^(p-2)s,p>1,ξ_i:R→R是连续的、不增的,0<ξ_1<ξ_2<…<ξ_(m-2)<ρ(T).利用Schauder不动点定理和上下解方法,证明了上述边值问题正解的一些存在性法则.这些结果在相应的微分方程(T=R)、差分方程(T=Z)以及通常的测度链上都是新的.特别是,如果非线性项容许变号,那么Sun和Li的结果[Appl.Math.Comput.,2006,182:478-491]仅仅是我们所得结果在相应微分方程(T=R)的一种特殊情形.作为应用,给出了一个例子验证了主要结果.
Aict f Finjte rmvedrig wave (M) so1uhons fOr the fOllowhg sechear syttem (I){u_t-u_(xx)+u^mv^p=0 u_t-v_(xx)+u^q=0 -∞0,p,q>0,m≥0 are studied. SolutiOns to (I) of the fOrm u (x, t)=lt(ct--x), v(x, t)=v (cl--X) are called W soIutiOns if there exjstS a fwite ', such that u({)=v(j)=0 for t<{,':=ct--x. It is proVed that if Pq+nl l. The asmpptohc weve profileS near the front as well as far from it are also determined. If I)q^m = l. the exjstence of travebe wave soluhons to (I) is proved. The plnof in Esqniruis's paper(1990) for the one m=0 co be sdriplified by using the methOd develOped in thjs paper.
