摘要
利用山路引理和喷泉定理容易得到当p(x)-Laplace方程有|u|p(x)-2u项时,方程解的存在性和多解性;当方程没有|u|p(x)-2u时,问题变得比较困难,利用最小作用原理得到无流边界p(x)-Laplace方程解的存在性,其中无流边界指的是{u=c,x∈Ω;∫Ω|▽u|p(x)-2(u/η)ds=0.
When a term of ｜u｜p（x）-2u is involved in p（x）-Laplace equation,it is easy to get the existence of solution and multiplicity of this equation using mountain pass theorem and fountain theorem.Otherwise,we apply the principle least action to obtain the existence of solution of p（x）-Laplace equation with no flux boundary,where no flux boundary is in the following：{u=c,x∈Ω;∫Ω｜▽u｜p（x）-2（u/η）ds=0.
出处
《四川理工学院学报（自然科学版）》
CAS
2011年第3期281-282,共2页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
甘肃省自然科学基金资助项目(096RJZE106)
