上饶师范学院学报
上饒師範學院學報
상요사범학원학보
JOURNAL OF SHANGRAO TEACHERS COLLEGE
2010年
6期
17-26
,共10页
p-Laplacian%对称临界性原理%不变集的方法%多解%变号解
p-Laplacian%對稱臨界性原理%不變集的方法%多解%變號解
p-Laplacian%대칭림계성원리%불변집적방법%다해%변호해
p-Laplacian%principle of symmetric criticality%invariant sets%multiple solutions%sign-changing solutions
考虑下面这个p-Laplacian问题多重变号解的存在性:-△pu+|u|(p-2)u=f(x,u) in RN,其中u∈W1,p(RN)(p≠2).我们结合对称临界性原理,不变集的方法和极小极大的方法,在f(x,u)关于u是奇的和其它的假设条件下,获得了上述问题的一个无界的径向对称的变号解序列.在N=4或N=6时,通过选择一个非径向对称子空间使得它包含的所有非零函数都是变号的,运用对称山路引理和对称临界性原理,获得了上述问题的一个无界的非径向对称的变号解序列.
攷慮下麵這箇p-Laplacian問題多重變號解的存在性:-△pu+|u|(p-2)u=f(x,u) in RN,其中u∈W1,p(RN)(p≠2).我們結閤對稱臨界性原理,不變集的方法和極小極大的方法,在f(x,u)關于u是奇的和其它的假設條件下,穫得瞭上述問題的一箇無界的徑嚮對稱的變號解序列.在N=4或N=6時,通過選擇一箇非徑嚮對稱子空間使得它包含的所有非零函數都是變號的,運用對稱山路引理和對稱臨界性原理,穫得瞭上述問題的一箇無界的非徑嚮對稱的變號解序列.
고필하면저개p-Laplacian문제다중변호해적존재성:-△pu+|u|(p-2)u=f(x,u) in RN,기중u∈W1,p(RN)(p≠2).아문결합대칭림계성원리,불변집적방법화겁소겁대적방법,재f(x,u)관우u시기적화기타적가설조건하,획득료상술문제적일개무계적경향대칭적변호해서렬.재N=4혹N=6시,통과선택일개비경향대칭자공간사득타포함적소유비령함수도시변호적,운용대칭산로인리화대칭림계성원리,획득료상술문제적일개무계적비경향대칭적변호해서렬.
In this paper, we study a p-Laplacian elliptic equation -△pu+|u|(p-2)u=f(x,u) in RN,u∈W1,p(RN)(P≠2). Applying Principle of Symmetric Criticality and the invariant set method, we obtain infinitely many radial sign-changing solutions for the above equation under some assumptions on f. Besides, using the symmetric Mountain Pass Theorem and Principle of Symmetric Criticality, we also obtain infinitely many nonradial sign-changing solutions for the above equation when N=4or N≥6.
