230
Views
0
CrossRef citations to date
0
Altmetric
Articles

Nehari type ground state solutions for periodic Schrödinger–Poisson systems with variable growth

ORCID Icon, &
Pages 856-871 | Received 05 Aug 2020, Accepted 26 Oct 2020, Published online: 28 Dec 2020

References

  • Zhikov VV. Averaging of functionals of the calculus of variations and elasticity theory. Math Ussr-izvestiya. 1987;29(1):33–66.
  • Chen YM, Levine S, Rao M. Variable exponent, linear growth functionals in image restoration. SIAM J Appl Math. 2006;66(4):1383–1406.
  • Antontsev SN, Rodrigues JF. On stationary thermo-rheological viscous flows. Annali Dell'Universitá Di Ferrara Sezione VII Scienze Matematiche. 2006;52(1):19–36.
  • Fragnelli G. Positive periodic solutions for a system of anisotropic parabolic equations. J Math Anal Appl. 2010;367(1):204–228.
  • Rrvivka M. Electrorheological fluids: modeling and mathematical theory. Berlin/Heidelberg: Springer; 2000.
  • Chen ST, Tang XH. Existence and multiplicity of solutions for Dirichlet problem of p(x)-Laplacian type without the Ambrosetti–Rabinowitz condition. J Math Anal Appl. 2020;123882. Available from: https://doi.org/10.1016/j.jmaa.2020.123882
  • Alves CO, Tavares LS. A Hardy-Littlewood-Sobolev-Type inequality for variable exponents and applications to quasilinear Choquard equations involving variable exponent. Mediterranean J Math. 2019;16(2):213.
  • Fan XL. p(x)-Laplacian equations in RN with periodic data and nonperiodic perturbations. J Math Anal Appl. 2008;341(1):103–119.
  • Rădulescu VD. Nonlinear elliptic equations with variable exponent: old and new. Nonlinear Anal: Theor Meth Appl. 2015;121:336–369.
  • Rădulescu VD, Repovs DD. Partial differential equations with variable exponents: variational methods and qualitative analysis. Vol. 9, Boca Raton (FL): CRC Press; 2015.
  • Chen ST, Fiscella A, Pucci P, et al. Semiclassical ground state solutions for critical Schrödinger-Poisson systems with lower perturbations. J Differ Equ. 2020;268(6):2672–2716.
  • Chen ST, Tang XHL. On the planar Schrödinger-Poisson system with the axially symmetric potential. J Differ Equ. 2020;268(3):945–976.
  • Qin DD, Tang XH. Two types of ground state solutions for periodic Schrödinger equations with zero on the boundary of the spectrum. Electronic J Differ Equ. 2015;2015(190):1–13.
  • Wen LX, Chen ST, Rădulescu VD. Axially symmetric solutions of the Schrödinger-Poisson system with zero mass potential in R2. Appl Math Lett. 2020;104:106244. 7.
  • Yoshida N. Picone identities for half-linear elliptic operators with p(x)-Laplacians and applications to Sturmian comparison theory. Nonlinear Anal: Theor Meth Appl. 2011;74(16):5631–5642.
  • Zang AH. p(x)-Laplacian equations satisfying Cerami condition. J Math Anal Appl. 2008;337(1):547–555.
  • Zhang QH. A strong maximum principle for differential equations with nonstandard p(x)-growth conditions. J Math Anal Appl. 2005;312(1):24–32.
  • Qin DD, Tang XH. Asymptotically linear Schrödinger equation with zero on the boundary of the spectrum. Electronic J Differ Equ. 2015;2015(213):1–15.
  • Qin DD, Tang XH. New conditions on solutions for periodic Schrödinger equations with spectrum zero. Taiwanese J Math. 2015;19(4):977–993.
  • Tang XH. Infinitely many solutions for semilinear Schrödinger equations with sign-changing potential and nonlinearity. J Math Anal Appl. 2013;401:407–415.
  • Tang XH. New super-quadratic conditions on ground state solutions for superlinear Schrödinger equation. Advanced Nonlinear Studies. 2014;14(2):349–361.
  • Tang XH. Non-Nehari manifold method for asymptotically linear Schrödinger equation. J Australian Math Soc. 2015;98(1):104–116.
  • Tang XH. Non-Nehari manifold method for asymptotically periodic Schrödinger equations. Science China Math. 2015;058(4):715–728.
  • Tang XH, Chen ST, Lin XY, et al. Ground state solutions of Nehari-Pankov type for Schrödinger equations with local super-quadratic conditions. J Differ Equ. 2020;268(8):4663–4690.
  • Chen ST, Tang XH. Berestycki-Lions conditions on ground state solutions for a nonlinear Schrödinger equation with variable potentials. Adv Nonlinear Anal. 2020;9(1):496–515.
  • Fan XL, Han XY. Existence and multiplicity of solutions for p(x)-Laplacian equations in RN. Nonlinear Anal: Theor Meth Appl. 2004;59(1–2):173–188.
  • Alves CO, Liu SB. On superlinear p(x)-Laplacian equations in RN. Nonlinear Anal Theor Meth Appl. 2010;73(8):2566–2579.
  • Liu SB, Li SJ. Infinitely many solutions for a superlinear elliptic equation. Acta Mathematica Sinica. 2003;4:
  • Jeanjean L, Tanaka K. Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities. Calc Var Partial Differ Equ. 2004;21(3):287–318.
  • Chen ST, Tang XH. Nehari type ground state solutions for asymptotically periodic Schrödinger-Poisson systems. Taiwanese J Math. 2017;21(2):363–383.
  • Li G, Rădulescu VD, Repovš DD, et al. Nonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz condition. Topol Methods Nonlinear Anal. 2018;51(1):55–77.
  • Diening L, Harjulehto P, Hästö P, et al. Lebesgue and Sobolev spaces with variable exponents. Heidelberg: Springer; 2011.
  • Fan XL, Zhao D. On the spaces Lp(x)(Ω) and Wm,p(x)(Ω). J Math Anal Appl. 2001;263(2):424–446.
  • Willem M. Minimax theorems. Boston (MA): Birkhäuser; 1996.
  • Fan XL, Shen JS, Zhao D. Sobolev embedding theorems for spaces Wk,p(x)(Ω). J Math Anal Appl. 2001;262(2):749–760.
  • Fan XL, Zhao YZ, Zhao D. Compact imbedding theorems with symmetry of Strauss–Lions type for the space W1,p(x)(Ω). J Math Anal Appl. 2001;255(1):333–348.
  • Benci V, Fortunato D. An eigenvalue problem for the Schrödinger-Maxwell equations. Topol Methods Nonlinear Anal. 1998;11(2):283–293.
  • Kichenassamy S, Véron L. Singular solutions of the p-Laplace equation. Mathematische Annalen. 1986;275(4):599–615.
  • de Thélin F. Local regularity properties for the solutions of a nonlinear partial differential equation. Nonlinear Anal Theor Meth Appl. 1982;6:839–844.
  • Cerami G, Vaira G. Positive solutions for some non-autonomous Schrödinger-Poisson systems. J Differ Equ. 2010;248(3):521–543.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.