四川大学学报（自然科学版）
四川大學學報（自然科學版）
사천대학학보（자연과학판）
JOURNAL OF SICHUAN UNIVERSITY（NATURAL SCIENCE EDITION）
2012年
3期
504-510
,共7页
常维p-Laplace系统%鞍点定理%Sobolev不等式%Wirtinger不等式
常維p-Laplace繫統%鞍點定理%Sobolev不等式%Wirtinger不等式
상유p-Laplace계통%안점정리%Sobolev불등식%Wirtinger불등식
p-Laplacian systems%saddle point theorem%Sobolev's inequality%Wirtinger's inequality (2000 MSC 34A34,34K13)
作者在自反一致凸Banach空间W1T·P中对一类具有非自治p次线性的常维p-Laplace系统进行了研究.不同于以往的非线性部分为超二次和次二次的情形,此系统的非线性部分F(t,x)=G(x)+H(t,x)满足p次线性,从而相应的泛函满足(PS)条件.利用临界点理论中的鞍点定理和极小作用原理,作者得到了此类系统的周期解的存在性,推广了已有的相关结果.
作者在自反一緻凸Banach空間W1T·P中對一類具有非自治p次線性的常維p-Laplace繫統進行瞭研究.不同于以往的非線性部分為超二次和次二次的情形,此繫統的非線性部分F(t,x)=G(x)+H(t,x)滿足p次線性,從而相應的汎函滿足(PS)條件.利用臨界點理論中的鞍點定理和極小作用原理,作者得到瞭此類繫統的週期解的存在性,推廣瞭已有的相關結果.
작자재자반일치철Banach공간W1T·P중대일류구유비자치p차선성적상유p-Laplace계통진행료연구.불동우이왕적비선성부분위초이차화차이차적정형,차계통적비선성부분F(t,x)=G(x)+H(t,x)만족p차선성,종이상응적범함만족(PS)조건.이용림계점이론중적안점정리화겁소작용원리,작자득도료차류계통적주기해적존재성,추엄료이유적상관결과.
In this paper,a class of ordinary p-Laplacian systems involving nonautonomous p-sublinear is studied in the reflexive and uniformly convex Banach space W1T·p,here nonlinearity F(t,x)=G(x)+ H (t,x) of these systems is p-sublinear which is different from suhquadractic and supquadractic conditions of references cited in this paper,therefore the corresponding functional to these systems satisfies (PS) condition.Then,existence results of periodic solutions for these systems are obtained by using the saddle point theorem and the least action principle in critical point theory.
