一类非线性基尔霍夫型方程的无穷多解Infinitely Many Solutions of a Class of Nonlinear Kirchhoff-type Equation
李莉;陈建清;
摘要(Abstract):
应用Clark定理和一些分析技巧讨论一类带有次临界指数的非线性基尔霍夫型问题:-(a+b∫_Ω|u|2dx)△u=λf(x,u)+|u|2dx)△u=λf(x,u)+|u|(p-2)u(4
*)的无穷多解.当f(x,u)满足一定的条件时,问题存在无穷多解.
关键词(KeyWords): Kirchhoff型问题;PS条件;Clark定理;无穷多解
基金项目(Foundation): 国家自然科学基金资助项目(11371091)
作者(Authors): 李莉;陈建清;
参考文献(References):
- [1]WU X.Existence of nontrivial and high energy solutions for Schrodinger-kirchhoff-type equations in RN[J].Nonlinear Anal Real World Appl,2011,12(2):1278-1287.
- [2]NIE J,WU X.Existence and multiplicity of non-trivial solutions for Schrodinger-Kirchhoff-type equations with adial potential[J].Nonlinear Anal,2012,75(8):3470-3479.
- [3]JIN J,WU X.Infinitely many radial solutions for Kirchhoff-type problems in RN[J].J Math Anal Appl,2010,369(2):564-574.
- [4]SUN J J,CHEN C L.Existence and multiplicity of solutions for Kirchhoff type equations[J].Nonlinear Anal,2011,74(4):1212-1222.
- [5]BITAO C.New existence and multiplicity of nontrivial solutions for nonlocal elliptic Kirchhoff type problems[J].Math Anal Appl,2012,394(2):488-495.
- [6]CLARK D C.A variant of the lusternik-Schnirelman theory[J].Indiana University Mathematics,1972,22(1):65-74.
- [7]BREMMER P.On Lp-Lq estimates for the wave equation[J].Math Z,1975,145(3):251-254.
- [8]SHU JIE L,WEN MING Z.Remarks on a class of elliptic problems with critical exponents[J].Nonlinear Anal,1998,32(6):769-774.