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Positive solutions to nonlinear systems involving fully nonlinear fractional operators

  • Pengcheng Niu , Leyun Wu EMAIL logo und Xiaoxue Ji
Veröffentlicht/Copyright: 9. Juni 2018
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Fractional Calculus and Applied Analysis
Aus der Zeitschrift Fractional Calculus and Applied Analysis Band 21 Heft 2

Abstract

In this paper we consider the following fractional system

F(x,u(x),v(x),Fα(u(x)))=0,G(x,v(x),u(x),Gβ(v(x)))=0,

where 0 < α, β < 2, 𝓕α and 𝓖β are the fully nonlinear fractional operators:

Fα(u(x))=Cn,αPV∫Rnf(u(x)−u(y))x−yn+αdy,Gβ(v(x))=Cn,βPV∫Rng(v(x)−v(y))x−yn+βdy.

A decay at infinity principle and a narrow region principle for solutions to the system are established. Based on these principles, we prove the radial symmetry and monotonicity of positive solutions to the system in the whole space and a unit ball respectively, and the nonexistence in a half space by generalizing the direct method of moving planes to the nonlinear system.

MSC 2010: 35B09; 35A01; 35B53; 35J47
Key Words and Phrases: nonlinear fractional system; fully nonlinear fractional operator; decay at infinity; narrow region principle; direct method of moving planes; radial symmetry; nonexistence

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11771354).

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Received: 2017-4-26
Published Online: 2018-6-9
Published in Print: 2018-4-25

© 2018 Diogenes Co., Sofia

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https://doi.org/10.1515/fca-2018-0030
Schlagwörter für diesen Artikel
nonlinear fractional system; fully nonlinear fractional operator; decay at infinity; narrow region principle; direct method of moving planes; radial symmetry; nonexistence

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 21–2–2018)
  4. Research Paper
  5. Initial-boundary value problems for fractional diffusion equations with time-dependent coefficients
  6. Research Paper
  7. Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms
  8. Research Paper
  9. Fractional generalizations of Zakai equation and some solution methods
  10. Research Paper
  11. Stability analysis of impulsive fractional difference equations
  12. Research Paper
  13. Mellin convolutions, statistical distributions and fractional calculus
  14. Research Paper
  15. Fractional wavelet frames in L2(ℝ)
  16. Research Paper
  17. Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions
  18. Research Paper
  19. Two point fractional boundary value problems with a fractional boundary condition
  20. Research Paper
  21. Large deviation principle for a space-time fractional stochastic heat equation with fractional noise
  22. Research Paper
  23. Extension of Mikhlin multiplier theorem to fractional derivatives and stable processes
  24. Research Paper
  25. Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications
  26. Research Paper
  27. Asymptotic behavior of mild solutions for nonlinear fractional difference equations
  28. Research Paper
  29. Positive solutions to nonlinear systems involving fully nonlinear fractional operators
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