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Fractional problems with critical nonlinearities by a sublinear perturbation

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Published/Copyright: May 9, 2020
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 23 Issue 2

Abstract

In this paper, the existence of two nontrivial solutions for a fractional problem with critical exponent, depending on real parameters, is established. The variational approach is used based on a local minimum theorem due to G. Bonanno. In addition, a numerical estimate on the real parameters is provided, for which the two solutions are obtained.

MSC 2010: Primary 35J60; Secondary 31B30; 35B33; 35B25
Key Words and Phrases: critical growth; fractional Laplacian problem; variational methods; local minimum

Acknowledgements

Lin Li is supported by Research Fund of National Natural Science Foundation of China (No. 11601046, 11861046), China Postdoctoral Science Foundation (No. 2019M662796), Chongqing Municipal Education Commission (No. KJQN20190081). The work of second author is in the frames of the projects DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution” of the Bulgarian National Science Fund and the bilateral agreement between Bulgarian Academy of Sciences and Serbian Academy of Sciences and Art.

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Received: 2019-08-28
Published Online: 2020-05-09
Published in Print: 2020-04-28

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Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 23–2–2020)
  4. Survey Paper
  5. Porous functions – II
  6. Research Paper
  7. On a non–local problem for a multi–term fractional diffusion-wave equation
  8. A class of linear non-homogenous higher order matrix fractional differential equations: Analytical solutions and new technique
  9. Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions
  10. Global existence and large time behavior of solutions of a time fractional reaction diffusion system
  11. Evaluation of fractional order of the discrete integrator. Part II
  12. Subordination principle for fractional diffusion-wave equations of Sobolev type
  13. Time-changed fractional Ornstein-Uhlenbeck process
  14. Fractional problems with critical nonlinearities by a sublinear perturbation
  15. New finite-time stability analysis of singular fractional differential equations with time-varying delay
  16. Reflection properties of zeta related functions in terms of fractional derivatives
  17. α-fractionally convex functions
  18. On the kinetics of Hadamard-type fractional differential systems
  19. Asymptotic stability of fractional difference equations with bounded time delays
  20. Short Paper
  21. The continuation of solutions to systems of Caputo fractional order differential equations
  22. Erratum
  23. Erratum: On modifications of the exponential integral with the Mittag-Leffler function
https://doi.org/10.1515/fca-2020-0023
Keywords for this article
critical growth; fractional Laplacian problem; variational methods; local minimum

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 23–2–2020)
  4. Survey Paper
  5. Porous functions – II
  6. Research Paper
  7. On a non–local problem for a multi–term fractional diffusion-wave equation
  8. A class of linear non-homogenous higher order matrix fractional differential equations: Analytical solutions and new technique
  9. Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions
  10. Global existence and large time behavior of solutions of a time fractional reaction diffusion system
  11. Evaluation of fractional order of the discrete integrator. Part II
  12. Subordination principle for fractional diffusion-wave equations of Sobolev type
  13. Time-changed fractional Ornstein-Uhlenbeck process
  14. Fractional problems with critical nonlinearities by a sublinear perturbation
  15. New finite-time stability analysis of singular fractional differential equations with time-varying delay
  16. Reflection properties of zeta related functions in terms of fractional derivatives
  17. α-fractionally convex functions
  18. On the kinetics of Hadamard-type fractional differential systems
  19. Asymptotic stability of fractional difference equations with bounded time delays
  20. Short Paper
  21. The continuation of solutions to systems of Caputo fractional order differential equations
  22. Erratum
  23. Erratum: On modifications of the exponential integral with the Mittag-Leffler function
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