[1] KIRCHHOFF G.Mechanik [M].Teubner:Leipzig,1883.
[2] LIONS J L.On some questions in boundary value problems of mathematical physics [J].Science Direct,1978,30:284-346.
[3] AROSIO A, PANIZZI S.On the well-posedness of the Kirchhoff string [J].Trans Amer Math Soc,1996,348(1):305-330.
[4] MAO A, ZHANG Z.Sign-changing and multiple solutions of Kirchhoff type problems without the P.S.condition [J].Nonlinear Analysis,2009,70:1275-1287.
[5] ZHANG J,TANG X H,ZHANG W.Infinitely many solutions of quasilinear Schrödinger equation with sign-changing potential [J].Journal of Mathematical Analysis and Applications,2014,420:1762-1775.
[6] XU L, CHEN H.Nontrivial solutions for Kirchhoff-type problems with a parameter [J].Journal of Mathematical Analysis and Applications,2016,433:455-472.
[7] PERERA K,ZHANG Z.Nontrivial solutions of Kirchhoff-type problems via the Yang index [J].Journal of Differential Equations,2006,221:246-255.
[8] CHEN S,LIU S.Standing waves for 4-superlinear Schrödinger-Kirchhoff equations [J].Mathematical Methods in the Applied Sciences.2014,38:2185-2193.
[9] LIU W,HE X.Multiplicity of high energy solutions for superlinear Kirchhoff equations [J].Journal of Applied Mathematics and Computing,2012,39:473-487.
[10] WU X.Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations inR3 [J].Nonlinear Analysis:Real World Applications,2011,12:1278-1287.
[11] HE X M,ZOU W M.Infinitely many positive solutions for Kirchhoff-type problems [J].Nonlinear Analysis,2009,70:1407-1414.
[12] BARTSCH T,WANG Z Q.Existence and multiplicity results for some superlinear elliptic problems on RN[J].Communications in Partial Differential Equations,1995,20:1725-1741.
[13] REED M,SIMON B.Methods of modern mathematical physics [M].Academic Press:Analysis of Operators,1978.
[14] CHANG K C.Infinite dimensional morse theory and multiple solution problems [M].Boston:Birkhäuser,2012.
[15] LIU Z,WANG Z Q.On Clark’s theorem and its applications to partially sublinear problems [J].Annales De Linstitut Henri Poinc are Analye Non Lineaire,2015,32:1015-1037. |
