Existence of Solutions to a Class of Kirchhoff-Type Equation with a General Subcritical Nonlinearity

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• 作者：Yong-Yi Lan
• 关键词：35J60 ; 35J25 ; Kirchhoff ; type equation ; subcritical growth ; variational methods ; the (C) condition ; mountain pass lemma
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：12
• 期：3
• 页码：851-861
• 全文大小：514 KB
• 参考文献：1.Kirchhoff, G.: Mechanik. Teubner, Leipzig (1883)
  2.Alves C.O., Corra F.J.S.A., Ma T.F.: Positive solutions for a quasilinear elliptic equation of Kirchhoff type. Comput. Math. Appl. 49, 85鈥?3 (2005)MathSciNet View Article MATH
  3.Perera K., Zhang Z.T.: Nontrivial solutions of Kirchhoff-type problems via the Yang index. J. Differ. Equ. 221(1), 246鈥?55 (2006)MathSciNet View Article MATH
  4.Mao A.M., Zhang Z.T.: Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition. Nonlinear Anal. 70(3), 1275鈥?287 (2009)MathSciNet View Article MATH
  5.He X.M., Zou W.M.: Multiplicity of solutions for a class of Kirchhoff type problems. Acta Math. Appl. Sin. Engl. Ser. 26(3), 387鈥?94 (2010)MathSciNet View Article MATH
  6.He X.M., Zou W.M.: Infinitely many positive solutions for Kirchhoff-type problems. Nonlinear Anal. 70(3), 1407鈥?414 (2009)MathSciNet View Article MATH
  7.Chen C.Y., Kuo Y.C., Wu T.F.: The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions. J. Differ. Equ. 250(4), 1876鈥?908 (2011)MathSciNet View Article MATH
  8.Cheng B.T., Wu X.: Existence results of positive solutions of Kirchhoff type problems. Nonlinear Anal. 71(10), 4883鈥?892 (2009)MathSciNet View Article MATH
  9.Sun J.J., Tang C.L.: Existence and multiplicity of solutions for Kirchhoff type equations. Nonlinear Anal. 74(4), 1212鈥?222 (2011)MathSciNet View Article MATH
  10.Sun J.J., Tang C.L.: Resonance problems for Kirchhoff type equations. Discrete Contin. Dyn. Syst. 33(5), 2139鈥?154 (2013)MathSciNet View Article MATH
  11.Xie Q.L., Wu X.P., Tang C.L.: Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent. Commun. Pure Appl. Anal. 12(6), 2773鈥?786 (2013)MathSciNet View Article MATH
  12.Yang Y., Zhang J.H.: Nontrivial solutions of a class of nonlocal problems via local linking theory. Appl. Math. Lett. 23(4), 377鈥?80 (2010)MathSciNet View Article MATH
  13.Zhang Z.T., Perera K.: Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow. J. Math. Anal. Appl. 317(2), 456鈥?63 (2006)MathSciNet View Article MATH
  14.Liang Z.P., Li F.Y., Shi J.P.: Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior. Ann. Inst. H Poincar茅 Anal. Non Lin茅aire 31, 155鈥?67 (2014)MathSciNet View Article MATH
  15.He X.M., Zou W.M.: Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3. J. Differ. Equ. 252, 1813鈥?834 (2012)MathSciNet View Article MATH
  16.Li Y.H., Li F.Y., Shi J.P.: Existence of a positive solution to Kirchhoff type problems without compactness conditions. J. Differ. Equ. 253, 2285鈥?294 (2012)View Article MATH
  17.Chen J.Q.: Multiple positive solutions to a class of Kirchhoff equation on R 3 with indefinite nonlinearity. Nonlinear Anal. 96, 135鈥?45 (2014)View Article
  18.Ye, Y.W., Tang, C.L.: (2013) Multiple solutions for Kirchhoff-type equation in R N . J. Math. Phys. 54, 081508
  19.Schechter M.: Superlinear elliptic boundary value problems. Manuscr. Math. 86, 253鈥?65 (1995)MathSciNet View Article MATH
  20.Rabinowitz, P.H.: Minimax methods in critical point theory with applications to differential equations. In: Conference Board of the Mathematical Sciences, vol. 65. American Mathematical Society, Providence, RI (1986)
  21.Willem, M.: Minimax Theorems. Birkh盲user, Boston (1996)
  22.Struwe, M.: Variational Methods, 2nd edn. Springer, Berlin (1996)
  
• 作者单位：Yong-Yi Lan (1)
  
  1. School of Sciences, Jimei University, Xiamen, 361021, People鈥檚 Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

This paper is devoted to the following nonlinear Kirchhoff-type problem $$-\bigg(a + b\int_{\Omega}|\nabla u|^{2}\,{d}x\bigg)\Delta u = \lambda f(x,u)$$