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Bifurcation properties for a class of fractional Laplacian equations in RN

Author

Listed:
  • Claudianor O. Alves
  • Romildo N. de Lima
  • Alânnio B. Nóbrega

Abstract

This paper concerns with the study of some bifurcation properties for the following class of nonlocal problems P (−Δ)su=λf(x)(u+h(u)),inRN,u(x)>0,forallx∈RN,lim|x|→∞u(x)=0,where N>2s, s∈(0,1), λ>0, f:RN→R is a positive continuous function, h:R→R is a bounded continuous function and (−Δ)su is the fractional Laplacian. The main tools used are the Leray–Shauder degree theory and the global bifurcation result due to Rabinowitz.

Suggested Citation

  • Claudianor O. Alves & Romildo N. de Lima & Alânnio B. Nóbrega, 2018. "Bifurcation properties for a class of fractional Laplacian equations in RN," Mathematische Nachrichten, Wiley Blackwell, vol. 291(14-15), pages 2125-2144, October.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:14-15:p:2125-2144
    DOI: 10.1002/mana.201700284
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    Cited by:

    1. César E. Torres Ledesma, 2022. "Existence of solutions for critical Fractional FitzHugh–Nagumo type systems," Mathematische Nachrichten, Wiley Blackwell, vol. 295(8), pages 1617-1640, August.
    2. Stefano Biagi & Alessandro Calamai & Gennaro Infante, 2023. "Nonzero positive solutions of fractional Laplacian systems with functional terms," Mathematische Nachrichten, Wiley Blackwell, vol. 296(1), pages 102-121, January.

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