纺织高校基础科学学报
紡織高校基礎科學學報
방직고교기출과학학보
BASIC SCIENCES JOURNAL OF TEXTILE UNIVERSITIES
2015年
2期
204-207,217
,共5页
p-Kirchhoff方程%喷泉定理%临界点%无穷多解
p-Kirchhoff方程%噴泉定理%臨界點%無窮多解
p-Kirchhoff방정%분천정리%림계점%무궁다해
p-Kirchhoff equation%Fountain T heorem%critical point%infinitely many solutions
研究一类带有凹凸非线性项的 p‐Kirchhoff 方程无穷多解的存在性。在Kirchhoff 函数 M以及权函数 f 满足更弱的假设下（即 M无正下界，权函数 f 不定号），利用RN 中两个重要的不等式证明能量泛函 J满足（PS ）c条件。结合喷泉定理，得到该方程的无穷多解的存在性，并且获得了一列能量无界的正能量解。拓展了 p‐Kirchhoff方程解的多重性结果。
研究一類帶有凹凸非線性項的 p‐Kirchhoff 方程無窮多解的存在性。在Kirchhoff 函數 M以及權函數 f 滿足更弱的假設下（即 M無正下界，權函數 f 不定號），利用RN 中兩箇重要的不等式證明能量汎函 J滿足（PS ）c條件。結閤噴泉定理，得到該方程的無窮多解的存在性，併且穫得瞭一列能量無界的正能量解。拓展瞭 p‐Kirchhoff方程解的多重性結果。
연구일류대유요철비선성항적 p‐Kirchhoff 방정무궁다해적존재성。재Kirchhoff 함수 M이급권함수 f 만족경약적가설하（즉 M무정하계，권함수 f 불정호），이용RN 중량개중요적불등식증명능량범함 J만족（PS ）c조건。결합분천정리，득도해방정적무궁다해적존재성，병차획득료일렬능량무계적정능량해。탁전료 p‐Kirchhoff방정해적다중성결과。
The existence of infinitely many solutions for a class of p‐Kirchhoff equations was studied .Assuming Kirchhoff function M and weight function f were weakened ,that is M has no positive lower bound and the sign of f is indefinite .It is proved that the energy functional J sat‐isfys the (PS)c condition by using two important inequalities in RN .Moreover ,the existence of infinitely many solutions was obtained by Fountain Theorem ,and a list of unbounded positive energy solutions was obtained .Thus ,the multiplicity result of solution for p‐Kirchhoff equa‐tions was extended .
