一类有界区域上分数阶p-Laplace方程解的多重性  

Multiple solutions for a class of fractional p-Laplacian problems on bounded domains

作　　者：鄢立旭 付永强[1] YAN Lixu;FU Yongqiang(Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2018年第5期524-529,共6页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11371110)

摘　　要：研究一类次临界增长的分数阶p-Laplace方程多重解的存在性。由于f(x,u)不满足Ambrosetti-Rabinowitz条件,方程的能量泛函I(u)不满足Palais-Smale条件。证明I(u)满足Cerami条件,利用山路引理的一种变形形式,分别在f(x,u)满足渐近线性增长和渐近超线性增长两种情形下,得到分数阶p-Laplace方程多重解的存在性。The existence of multiple solutions for the fractional p-Laplacian equations with sub-critical growth is considered. Because of the lack of an Ambrosetti-Rabinowitz type condition on f( x,u),the energy functional I( u) doesn’t satisfy the Palais-Smale condition. It is shown that I( u) satisfies the Cerami condition. By means of a variant of Mountain Pass Theorem,the existence of multiple solutions for the fractional p-Laplacian equations is obtained for the two cases of asymptotic linear growth and asymptotic superlinear growth.

关 键 词：分数阶P-Laplace方程 解的多重性 变分法 山路引理 

分 类 号：O175.29[理学—数学]