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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 9
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Articles

Three solutions for a nonlocal fractional p-Kirchhoff type elliptic system

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Pages 1871-1888 | Received 26 Apr 2019, Accepted 16 Sep 2019, Published online: 26 Sep 2019

References

  • Kirchhoff G. Vorlesungen über Mechanik. Leipzig: Teubner; 1883.
  • Chipot M, Lovat B. Some remarks on non local elliptic and parabolic problems. Nonlinear Anal TMA. 1997;30:4619–4627. doi: 10.1016/S0362-546X(97)00169-7
  • Alves CO, Corrâa FSJA, Ma TF. Positive solutions for a quasilinear elliptic equations of Kirchhoff type. Comput Math Appl. 2005;49:85–93. doi: 10.1016/j.camwa.2005.01.008
  • Graef JR, Heidarkhani S, Kong L. A variational approach to a Kirchhoff-type problem involving two parameters. Results Math. 2013;63:877–889. doi: 10.1007/s00025-012-0238-x
  • Ricceri B. On an elliptic Kirchhoff-type problem depending on two parameters. J Global Optim. 2010;46:543–549. doi: 10.1007/s10898-009-9438-7
  • Chen Y, Levine S, Rao M. Variable exponent linear growth functionals in image processing. SIAM J Appl Math. 2006;66:1383–1406. doi: 10.1137/050624522
  • Diening L. Theorical and numerical results for electrorheological fluids [Ph.D. thesis]. Germany: University of Freiburg; 2002.
  • Halsey TC. Electrorheological fluids. Science. 1992;258:761–766. doi: 10.1126/science.258.5083.761
  • Correa FJSA, Nascimento RG. On a nonlocal elliptic system of p-Kirchhoff-type under Neumann boundary condition. Math Comput Model. 2009;49(3–4):598–604. doi: 10.1016/j.mcm.2008.03.013
  • Chen CY, Kuo YC, Wu TF. The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions. J Differ Equ. 2011;250(4):1876–1908. doi: 10.1016/j.jde.2010.11.017
  • Corrêa FJSA, Figueiredo GM. On a p-Kirchhoff equation via Krasnoselskiiś genus. Appl Math Lett. 2009;22(6):819–822. doi: 10.1016/j.aml.2008.06.042
  • Liu DC. On a p-Kirchhoff-type equation via fountain theorem and dual fountain theorem. Nonlinear Anal. 2010;72:302–308. doi: 10.1016/j.na.2009.06.052
  • Ma TF. Remarks on an elliptic equation of Kirchhoff type. Nonlinear Anal. 2005;63:1967–1977. doi: 10.1016/j.na.2005.03.021
  • Sun JJ, Tang CL. Existence and multiplicity of solutions for Kirchhoff type equations. Nonlinear Anal. 2011;74(4):1212–1222. doi: 10.1016/j.na.2010.09.061
  • Cheng B, Wu X, Liu J. Multiplicity of solutions for nonlocal elliptic system of (p,q)-Kirchhoff type. Abstract Appl Anal. 2011. doi:10.1155/2011/526026.
  • Chen W, Deng S. The Nehari manifold for a fractional p-Laplacian system involving concave–convex nonlinearities. Nonlinear Anal Real World Appl. 2016;27:80–92. doi: 10.1016/j.nonrwa.2015.07.009
  • Ricceri B. A further three critical points theorem. Nonlinear Anal. 2009;71(9):4151–4157. doi: 10.1016/j.na.2009.02.074
  • Adams RA. Sobolev spaces. New York: Academic Press, 1975.
  • Demengel F, Demengel G, Erné R. Functional spaces for the theory of elliptic partial differential equations. London: Springer; 2012.
  • Nezza ED, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136(5):521–573. doi: 10.1016/j.bulsci.2011.12.004
  • Barrios B, Colorado E, De Pablo A. On some critical problems for the fractional Laplacian operator. J Differ Equ. 2012;252:6133–6162. doi: 10.1016/j.jde.2012.02.023
  • Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York: Universitext, Springer; 2011.
  • Zeidler E. Nonlinear functional analysis and applications, in nonlinear monotone operators. Vol. II/B. New York: Springer-Verlag; 1990.

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