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Infinitely many solutions for fractional Schr\"odinger equation with superquadratic conditions or combined nonlinearities

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초록

We obtain infinitely many solutions for a class of fractional Schr\"odinger equation, where the nonlinearity is superquadratic or involves a combination of superquadratic and subquadratic terms at infinity. By using some weaker conditions, our results extend and improve some existing results in the literature.

Abstract

We obtain infinitely many solutions for a class of fractional Schr\"odinger equation, where the nonlinearity is superquadratic or involves a combination of superquadratic and subquadratic terms at infinity. By using some weaker conditions, our results extend and improve some existing results in the literature.

참고문헌 (34)

  1. V. Ambrosio, "Ground states for superlinear fractional Schrodinger equations in RN", Ann. Acad. Sci. Fenn. Math, 41(2), pp.745~756 (2016)[DOI]
  2. V. Ambrosio, "Multiple solutions for a fractional p-Laplacian equation with sign-changing potential", Electron. J. Dierential Equations, pp.12~ (2016)
  3. V. Ambrosio, "Sign-changing solutions for a class of Schrodinger equations with vanishing potentials", Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl, 29(1), pp.127~152 (2018)[DOI]
  4. P. Bartolo, "Abstract critical point theorems and applications to some nonlinear problems with \strong"resonance at innity", Nonlinear Anal, 7(9), pp.981~1012 (1983)[DOI]
  5. T. Bartsch, "Handbook of Dierential equations-Stationary Partial Dierential Equations, Vol. 2", pp.1~55 (2005), Elsevier
  6. H. Berestycki, "Nonlinear scalar eld equations. I. Existence of a ground state", Arch. Rational Mech. Anal, 82(4), pp.313~345 (1983)[DOI]
  7. C. Chen, "Innitely many solutions for fractional Schrodinger equations in RN", Electron. J. Dierential Equations, 2016, pp.15~ (2016)
  8. J. Chen, "Innitely many solutions for fractional Schrodinger-Poisson systems with sign-changing potential", Electron. J. Dierential Equations, 2017, pp.13~ (2017)
  9. B. Cheng, "New existence of solutions for the fractional p-Laplacian equations with sign-changing potential and nonlinearity", Mediterr. J. Math, 13(5), pp.3373~3387 (2016)[DOI]
  10. CRC Financial Mathematics Series, "Chapman &Hall", pp.CRC, R. Cont
  11. E. Di Nezza, "Hitchhiker's guide to the fractional Sobolev spaces", Bull. Sci. Math, 136(5), pp.521~573 (2012)[DOI]
  12. X. Du, "Existence and multiplicity of nontrivial solutions for a class of semilinear fractional Schrodinger equations", J. Funct. Spaces, 2017, pp.7~ (2017)[DOI]
  13. M. Du, "Innitely many solutions of the nonlinear fractional Schrodinger equations", Discrete Contin. Dyn. Syst. Ser. B, 21(10), pp.3407~3428 (2016)[DOI]
  14. P. Felmer, "Positive solutions of the nonlinear Schrodinger equation with the fractional Laplacian", Proc. Roy. Soc. Edinburgh Sect. A, 142(6), pp.1237~1262 (2012)[DOI]
  15. M. Jara, "Nonequilibrium scaling limit for a tagged particle in the simple exclusion process with long jumps", Comm. Pure Appl. Math, 62(2), pp.198~214 (2009)[DOI]
  16. L. J. Jia, "Multiplicity solutions of a class fractional Schrodinger equations", Open Math, 15(1), pp.1010~1023 (2017)[DOI]
  17. H. Jin, "Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth", Electron. J. Dierential Equations, 2017, pp.19~ (2017)
  18. S. Khoutir, "Existence of innitely many high energy solutions for a fractional Schrodinger equation in RN", Appl. Math. Lett, 61, pp.156~162 (2016)[DOI]
  19. N. Laskin, "Fractional quantum mechanics and Levy path integrals", Phys. Lett. A, 268(4-6), pp.298~305 (2000)[DOI]
  20. N. Laskin, "Fractional Schrodinger equation", Phys. Rev. E, 66(5), pp.7~ (2002)[DOI]
  21. P. H. Rabinowitz, "Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, 65", Published for the Conference Board of the Mathematical Sciences (1986)
  22. P. H. Rabinowitz, "On a class of nonlinear Schrodinger equations", Z. Angew. Math. Phys, 43(2), pp.270~291 (1992)[DOI]
  23. S. Secchi, "Ground state solutions for nonlinear fractional Schrodinger equations in RN", J. Math. Phys, 54(3), pp.17~ (2013)[DOI]
  24. S. Secchi, "On fractional Schrodinger equations in RN without the Ambrosetti-Rabinowitz condition", Topol. Methods Nonlinear Anal, 47(1), pp.19~41 (2016)
  25. W. A. Strauss, "Existence of solitary waves in higher dimensions", Comm. Math. Phys, 55(2), pp.149~162 (1977)
  26. K. Teng, "Multiple solutions for a class of fractional Schrodinger equations in RN", Nonlinear Anal. Real World Appl, 21, pp.76~86 (2015)[DOI]
  27. C. E. Torres Ledesma, "Existence and concentration of solutions for a non-linear fractional Schrodinger equation with steep potential well", Commun. Pure Appl. Anal, 15(2), pp.535~547 (2016)[DOI]
  28. H. Weitzner, "Some applications of fractional equations", Commun. Nonlinear Sci. Numer. Simul, 8(3-4), pp.273~281 (2003)[DOI]
  29. M. Willem, "Minimax theorems", Progress in Nonlinear Dierential Equations and their Applications, 24 (1996), Birkhauser Boston, Inc[DOI]
  30. M. -H. Yang, "Innitely many homoclinic solutions for second-order Hamiltonian systems with odd nonlinearities", Nonlinear Anal, 74(7), pp.2635~2646 (2011)[DOI]
  31. H. Zhang, "Existence and multiplicity of solutions for superlinear fractional Schrodinger equations in RN", J. Math. Phys, 56(9), pp.13~ (2015)[DOI]
  32. "2015", ~
  33. "2015", ~
  34. Y. Zhang, "Existence of innitely many solutions for fractional p-Laplacian equations with sign-changing potential", Electron. J. Dierential Equations, 2017, pp.14~ (2017)

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