带有对数非线性项的p-Kirchhoff型方程的多解性
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摘要
研究了一类带有对数非线性项的p-Kirchhoff型方程的多解性问题.利用山路定理,Ekeland变分原理和对数Sobolev不等式,在有界区上讨论了方程非平凡解的多重性,证明了泛函满足山路定理的条件,结合Ekeland变分原理,得到结论方程至少含有两个非平凡解.
Multiple solutions for p-Kirchhoff equation with logarithmic nonlinearity were investigated.Multiplicity of nontrivial solutions were discussed on a bounded domain by Mountain Pass Theorem,Ekeland's variational principle and logarithmic Sobolev inequality.It proved that the functional satisfied conditions of Mountain Pass Theorem and combined with Ekeland's variational principle,it drew a conclusion that the problem had at least two nontrivial solutions.
Multiple solutions for p-Kirchhoff equation with logarithmic nonlinearity were investigated.Multiplicity of nontrivial solutions were discussed on a bounded domain by Mountain Pass Theorem,Ekeland's variational principle and logarithmic Sobolev inequality.It proved that the functional satisfied conditions of Mountain Pass Theorem and combined with Ekeland's variational principle,it drew a conclusion that the problem had at least two nontrivial solutions.
引文
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[10]Radulescu V D,Xiang M,Zhang B.Existence of solutions for abi-nonlocal fractional p-Kirchhoff type problem[J].Computers and Mathematics with Applications,2016,71(1):255-266.
[11]Ji C,Szulkin A.A logarithmic Schrdinger equation with asymptotic conditions on the potential[J].Journal of Mathematical Analysis and Applications,2016,437(1):241-254.
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[2]Mao A,Luan S.Sign-changing solutions of aclass of nonlocal quasilinear elliptic boundary value problems[J].Journal of Mathematical Analysis and Applications,2011,383(1):239-243.
[3]Zhang Z,PereraK.Sign changing solutions of Kirchhoff type problems viainvariant sets of descent flow[J].Journal of Mathematical Analysis and Applications,2006,317(2):456-463.
[4]Li Y,Li F,Shi J.Existence of apositive solution to Kirchhoff type problems without compactness conditions[J].Journal of Differential Equations,2012,253(7):2285-2294.
[5]Sun J J,Tang C L.Existence and multiplicity of solutions for Kirchhoff type equations[J].Nonlinear Analysis Theory Methods and Applications,2011,74(4):1212-1222.
[6]Chen C Y,Kuo Y C,Wu T F.The Nehari manifold for aKirchhoff type problem involving sign-changing weight functions[J].Journal of Differential Equations,2011,250(4):1876-1908.
[7]Júlio F.On an elliptic equation of p-Kirchhoff type via variational methods[J].Bulletin of the Australian Mathematical Society,2006,74(2):263-277.
[8]Júlio F,Figueiredo G M.On an elliptic equation of pKirchhoff type viavariational methods[J].Bulletin of the Australian Mathematical Society,2006,74(2):263-277.
[9]李健,杜泊船,赵昕,等.p-Kirchhoff型方程解的多重性[J].吉林大学学报,2013,51(4):580-584.Li Jian,Du Bochuan,Zhao Xin,et al.Multiplicity of solution of p-Kirchhoff type equation[J].Journal of Jilin University,2013,51(4):580-584.(in Chinese)
[10]Radulescu V D,Xiang M,Zhang B.Existence of solutions for abi-nonlocal fractional p-Kirchhoff type problem[J].Computers and Mathematics with Applications,2016,71(1):255-266.
[11]Ji C,Szulkin A.A logarithmic Schrdinger equation with asymptotic conditions on the potential[J].Journal of Mathematical Analysis and Applications,2016,437(1):241-254.
[12]SquassinaM,Szulkin A.Multiple solutions to logarithmic Schrdinger equations with periodic potential[J].Calculus of Variations and Partial Differential Equations,2015,54(1):585-597.
[13]Cong N L,Xuan T L.Global solution and blow-up for aclass of p-Laplacian evolution equations with logarithmic nonlinearity[J].Computers and Mathematics with Applications,2017,73(9):1-21.