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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 1
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Articles

Three solutions for a differential inclusion problem involving the p(x)-Kirchhoff-type

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Pages 60-71 | Received 08 Feb 2011, Accepted 18 May 2011, Published online: 27 Jun 2011

References

  • Ružička , M . 2000 . Electrortheological Fluids: Modeling and Mathematical Theory , Berlin : Springer-Verlag .
  • Zhikov , VV . 1987 . Averaging of functionals of the calculus of variations and elasticity theory . Math. USSR. Izv. , 9 : 33 – 66 .
  • Dai , GW and Hao , RF . 2009 . Existence of solutions for a p(x)-Kirchhoff-type equation . J. Math. Anal. Appl. , 359 : 275 – 284 .
  • Fan , XL and Zhao , D . 2001 . On the space L p(x)(Ω) and W k,p(x)(Ω) . J. Math. Anal. Appl. , 263 : 424 – 446 .
  • Fan , XL . 2007 . On the sub-supersolition methods for p(x)-Laplacian equations . J. Math. Anal. Appl. , 330 : 665 – 672 .
  • Fan , XL and Zhang , QH . 2005 . Eigenvalues of p(x)-Laplacian Dirichlet problem . J. Math. Anal. Appl. , 302 : 306 – 317 .
  • Fan , XL and Zhao , D . 1998 . On the generalized Orlicz–Sobolev spaces W k,p(x)(Ω) . J. Gansu Educ. College. , 12 ( 1 ) : 1 – 6 .
  • Ge , B , Xue , XP and Zhou , QM . 2010 . The existence of radial solutions for differential inclusion problems in ℝ N involving the p(x)-Laplacian . Nonlinear Anal. , 73 : 622 – 633 .
  • Ge , B and Xue , XP . 2010 . Multiple solutions for inequality Dirichlet problems by the p(x)-Laplacian . Nonlinear Anal: R.W.A. , 11 : 3198 – 3210 .
  • Ge , B , Xue , XP and Zhou , QM . 2010 . Three solutions to inequalities of Dirichlet problem driven by p(x)-Laplacian . Appl. Math. Mech.-Engl. Ed. , 31 : 1283 – 1292 .
  • Ge , B and Zhou , QM . 2011 . Existence and multiplicity of solutions for a Neumann-type p(x)-Laplacian equation with nonsmooth potential . E. J. Qualitative Theory Diff. Equ. , 17 : 1 – 10 .
  • Dai , GW and Liu , WL . 2009 . Three solutions for a differential inclusion problem involving the p(x)-Laplacian . Nonlinear Anal. , 71 : 5318 – 5326 .
  • Dai , GW . 2009 . Three solutions for a Neumann-type differential inclusion problem involving the p(x)-Laplacian . Nonlinear Anal. , 70 : 3755 – 3760 .
  • Cammaroto , F and Vilasi , L . 2011 . Multiple solutions for a Kirchhoff-type problem involving the p(x)-Laplacian operator . Nonlinear Anal. , 70 : 1841 – 1852 .
  • Ricceri , B . 2009 . A further three critical points theorem . Nonlinear Anal. , 71 ( 9 ) : 4151 – 4157 .
  • Clarke , FH . 1983 . Optimization and Nonsmooth Analysis , New York : Wiley .
  • Bonanno , G and Giovannelli , N . 2005 . An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities . J. Math. Anal. Appl. , 308 : 596 – 604 .
  • Bonanno , G and Candito , P . 2004 . On a class of nonlinear variational-hemivariationa linequalities . Appl. Anal. , 83 : 1229 – 1244 .
  • Chang , CK . 1981 . Variational methods for non-differentiable functionals and their applications to partial differential equations . J. Math. Anal. Appl. , 80 ( 1 ) : 102 – 129 .
  • Dai , GW and Ma , RY . 2011 . Solutions for a p(x)-Kirchhoff type equation with Neumann boundary data. Nonlinear Anal: R.W.A. 12 , : 2666 – 2680 .

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