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A unique weak solution for a kind of coupled system of fractional Schrodinger equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we prove the existence of a unique weak solution for a class of fractional systems of Schrodinger equations by using the Minty-Browder theorem in the Cartesian space. To this aim, we need to impose some growth conditions to control the source functions with respect to dependent variables.
Rocznik
Strony
313--322
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Department of Pure Mathematics Faculty of Science Imam Khomeini International University P.O. Box 34149-16818, Qazvin, Iran
  • Department of Pure Mathematics Faculty of Science Imam Khomeini International University P.O. Box 34149-16818, Qazvin, Iran
Bibliografia
  • [1] F. Abdolrazaghi, A. Razani, On the weak solutions of an overdetermined system of nonlinear fractional partial integro-differential equations, Miskolc Math. Notes 20 (2019), 3-16.
  • [2] G. Autuori, P. Pucci, Elliptic problems involving the fractional Laplacian in HŁN, J. Differential Equations 255 (2013), 2340-2362.
  • [3] B. Barrios, E. Colorado, A. De Pablo, U. Sanchez, On some critical problems for the fractional Laplacian operator, J. Differential Equations 252 (2012), 6133-6162.
  • [4] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer Science & Business Media, 2010.
  • [5] L. Caffarelli, L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), 1245-1260.
  • [6] X. Chang, Ground state solutions of asymptotically linear fractional Schrodinger equations, J. Math. Phys. 54 (2013), 061504.
  • [7] X. Chang, Z. Wang, Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity, Nonlinearity 26 (2013), 479-494.
  • [8] K. Diethelm, The Analysis of Fractional Differential Equations: An application-oriented exposition using differential operators of Caputo type, Springer Science & Business Media, 2010.
  • [9] S. Dipierro, G. Palatucci, E. Valdinoci, Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian, arXiv:1202.0576, (2012).
  • [10] P. Felmer, A. Quaas, J. Tan, Positive solutions of the nonlinear Schrodinger equation with the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), 1237-1262.
  • [11] A. Fiscella, P. Pucci, S. Saldi, Existence of entire solutions for Schrddinge.r-Ha.rdy systems involving two fractional operators, Nonlinear Anal. 158 (2017), 109-131.
  • [12] A. Fiscella, P. Pucci, B. Zhang, p-fractional Hardy-Schrodinger-Kirchhoff systems with critical nonlinearities, Adv. Nonlinear Anal. 8 (2019) 1, 1111-1131.
  • [13] Y. Fu, H. Li, P. Pucci, Existence of nonnegative solutions for a class of systems involving fractional (p,q)-Laplacian operators, Chin. Ann. Math. Ser. B 39 (2018), 357-372.
  • [14] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, 2006.
  • [15] N. Nyamoradi, A. Razani, Existence of solutions for a new p-Laplacian fractional boundary value problem with impulsive effects, Journal of New Researches in Mathematics 5 (2019), 117-128.
  • [16] I. Podlubny, The Laplace transform, method for linear differential equations of the fractional order, arXiv:funct-an/9710005, (1997).
  • [17] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, vol. 198, Academic Press, San Diego, California, USA, 1999.
  • [18] A. Razani, Weak and strong detonation profiles for a qualitative model, J. Math. Anal. Appl. 276 (2002), 868-881.
  • [19] A. Razani, Weak Chapman- Jouguet detonation profile for a qualitative model, Bull. Aust. Math. Soc. 66 (2002), 393-403.
  • [20] A. Razani, Existence of Chapman-Jouguet detonation for a viscous combustion model J. Math. Anal. Appl. 293 (2004), 551-563.
  • [21] A. Razani, Shock waves in gas dynamics, Surv. Math. Appl. 2 (2007), 59-89.
  • [22] A. Razani, Chapman-Jouguet travelling wave for a two-steps reaction scheme, Ital. J. Pure Appl. Math. 39 (2018), 544-553.
  • [23] A. Razani, Subsonic detonation waves in porous media, Phys. Scr. 94 (2019), no. 085209.
  • [24] S. Secchi, On fractional Schrodinger equations in RN without the Ambrosetti-Rabinowitz condition, arXiv:1210.0755 (2012).
  • [25] R. Servadei, E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian, Trans. Amer. Math. Soc. 367 (2015), 67-102.
  • [26] J. Tan, Y. Wang, J. Yang, Nonlinear fractional field equations, Nonlinear Anal. 75 (2012), 2098-2110.
  • [27] J. Xu, Z. Wei, W. Dong, Existence of weak solutions for a fractional Schrodinger equation, Commun. Nonlinear Sci. Numer. Simul. 22 (2015), 1215-1222.
  • [28] Q. Yang, F. Liu, I. Turner, Numerical methods for fractional partial differential equations with Riesz space fractional derivatives, Appl. Math. Model. 34 (2010), 200-218.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9eca1156-9274-44b0-9317-8cb061416de9
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