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Infinitely many large energy solutions of nonlinear Schr$\ddot{o}$dinger-Maxwell system

Year 2014, Volume: 2 Issue: 2, 87 - 94, 01.08.2014

Abstract

This paper deals with the existence of infinitely many large energy solutions for nonlinear Schrödinger-Maxwell system { −∆ + ( ) + = | | −1 in ℝ−∆ = in ℝ

References

  • A. AMBROSETTI, D.RUIZ, multiple bound states for the Schrödinger-Poisson problem, Commun. Contemp. Math., 10(3) (2008), 391–404.
  • A. AZZOLINI, P. D’AVENIA, A. POMPONIO, On the Schrödinger-Maxwell equations under effect of a general nonlinear term, Ann. Inst. H. Poincare Anal. Non Lineair., 27(2) (2010), 779–791.
  • T. D’APRIL, D. MUGNAL, Solitary waves for nonlinear Klein-Gordon-Maxwell and Schördinger-Maxwell equations, Proc.Roy.Soc.Edinburgh. Sect. (A)., 134(5) (2004), 893–906.
  • A. AMBROSETTI, A. MALCHIODI, Perturbation Methods and Semilinear Elliptic Problems on R^n, Progr. Math. Birkhuser Verlag, Vol. 240 (2006).
  • A. AZZOLINI, A. POMPONIO, Ground staes solutions for the nonlinear Schördinger-Maxwell equations, J.Math. Anal. Appl., 345(1) (2008), 90–108.
  • V.BENCI, D. FORTUNATO, An eigenvalue problem for the Schördinger-Maxwell equations ,Topol.Methods nonlinear Anal., 11(2) (1998), 283–293.
  • TH. BARTHS, SH. PENG, Semiclassical symmetric Schrdinger equations: existence of solutions concentrating simultaneously on several spheres, Z. Angew. Math. Phys., 58(5) (2007), 778–804.
  • D. BONHEURE, J. VAN SCHAFTINGEN, Bound state solutions for a class of nonlinear Schrdinger equations, Rev. Mat. Iberoam., 24 (2008), 297–351.
  • V. BENCI, D. FORTUNATO, A. MASIELLO, L. PISANI, Solitons and the electromagneticfield, Math. Z., 232(1) (1999), 73–102.
  • D. BONHEURE, J.DI COSMO, J.VAN SCHAFTINGEN, Nonlinear Schrdinger equation with unbounded or vanishing potentials: Solutions concentrating on lower dimensional spheres, J.Differential Equations., 252 (2012) , 941–968.
  • G.M. COCLITE, A multiplicity result for the nonlinear Schrödinger -Maxwell equations, Commun. Apll.Anal., 7(2-3) (2003), 417–423.
  • G. CERAMI, An existence criterion for the points on unbounded manifolds, Istit. Lombardo Accad. Sci. Lett. Rend. A ., 112(2) (1979), 332– 336.
  • S.J. CHEN, C.L. TANG, High energy solutions for the superlinear Schrödinger-Maxwell ewuations, Nonlinear Anal., 71(10) (2009), 4927– 4934.
  • D. GILBARG, N.S. TRUDINGER, Elliptic partial differential equations of second order, Classics in Mathematics. Springer-Verlag, Berlin, (2001).
  • Y.JIANG, ZH. WANG, H-S ZHOU, multiple solutions for a nonhomogeneous Schrödinger-Maxwell system in R^3, arXiv: 1204.3359v1 [math.AP], 16Apr (2012).
  • L.LI, SH-J. CHEN, Infinitely many large energy solutions of superlinear Schrödinger-maxwell equations, Electron. j. Differential Equations., Vol.(2012) No. 224 (2012), 1–9.
  • D. RUIZ, The Schrödinger-Poisson equation under effect of nonlinear local term, J. Funct. Anal., 232(2) (2006), 655–674.
  • F.K. ZHAO, Y.H. DING, On Hamiltonian elliptic systes with periodic and non-periodic potentials, J.Differential Equations., 249 (2010) , 2964–2985.
  • J. ZHANG, W. QIN, F. ZHAO, Existence and multiplicity of solutions for asymptotically linear nonpreiodic Hamiltonian elliptic system, J. Math. Anal. Appl., 399 (2013), 433-441.
  • W. M. ZOU, M. SCHECHETER, Critical point theory and its applications, Springer, New York (2006).

Infinitely many large energy solutions of nonlinear Schrödinger

Year 2014, Volume: 2 Issue: 2, 87 - 94, 01.08.2014

Abstract

References

  • A. AMBROSETTI, D.RUIZ, multiple bound states for the Schrödinger-Poisson problem, Commun. Contemp. Math., 10(3) (2008), 391–404.
  • A. AZZOLINI, P. D’AVENIA, A. POMPONIO, On the Schrödinger-Maxwell equations under effect of a general nonlinear term, Ann. Inst. H. Poincare Anal. Non Lineair., 27(2) (2010), 779–791.
  • T. D’APRIL, D. MUGNAL, Solitary waves for nonlinear Klein-Gordon-Maxwell and Schördinger-Maxwell equations, Proc.Roy.Soc.Edinburgh. Sect. (A)., 134(5) (2004), 893–906.
  • A. AMBROSETTI, A. MALCHIODI, Perturbation Methods and Semilinear Elliptic Problems on R^n, Progr. Math. Birkhuser Verlag, Vol. 240 (2006).
  • A. AZZOLINI, A. POMPONIO, Ground staes solutions for the nonlinear Schördinger-Maxwell equations, J.Math. Anal. Appl., 345(1) (2008), 90–108.
  • V.BENCI, D. FORTUNATO, An eigenvalue problem for the Schördinger-Maxwell equations ,Topol.Methods nonlinear Anal., 11(2) (1998), 283–293.
  • TH. BARTHS, SH. PENG, Semiclassical symmetric Schrdinger equations: existence of solutions concentrating simultaneously on several spheres, Z. Angew. Math. Phys., 58(5) (2007), 778–804.
  • D. BONHEURE, J. VAN SCHAFTINGEN, Bound state solutions for a class of nonlinear Schrdinger equations, Rev. Mat. Iberoam., 24 (2008), 297–351.
  • V. BENCI, D. FORTUNATO, A. MASIELLO, L. PISANI, Solitons and the electromagneticfield, Math. Z., 232(1) (1999), 73–102.
  • D. BONHEURE, J.DI COSMO, J.VAN SCHAFTINGEN, Nonlinear Schrdinger equation with unbounded or vanishing potentials: Solutions concentrating on lower dimensional spheres, J.Differential Equations., 252 (2012) , 941–968.
  • G.M. COCLITE, A multiplicity result for the nonlinear Schrödinger -Maxwell equations, Commun. Apll.Anal., 7(2-3) (2003), 417–423.
  • G. CERAMI, An existence criterion for the points on unbounded manifolds, Istit. Lombardo Accad. Sci. Lett. Rend. A ., 112(2) (1979), 332– 336.
  • S.J. CHEN, C.L. TANG, High energy solutions for the superlinear Schrödinger-Maxwell ewuations, Nonlinear Anal., 71(10) (2009), 4927– 4934.
  • D. GILBARG, N.S. TRUDINGER, Elliptic partial differential equations of second order, Classics in Mathematics. Springer-Verlag, Berlin, (2001).
  • Y.JIANG, ZH. WANG, H-S ZHOU, multiple solutions for a nonhomogeneous Schrödinger-Maxwell system in R^3, arXiv: 1204.3359v1 [math.AP], 16Apr (2012).
  • L.LI, SH-J. CHEN, Infinitely many large energy solutions of superlinear Schrödinger-maxwell equations, Electron. j. Differential Equations., Vol.(2012) No. 224 (2012), 1–9.
  • D. RUIZ, The Schrödinger-Poisson equation under effect of nonlinear local term, J. Funct. Anal., 232(2) (2006), 655–674.
  • F.K. ZHAO, Y.H. DING, On Hamiltonian elliptic systes with periodic and non-periodic potentials, J.Differential Equations., 249 (2010) , 2964–2985.
  • J. ZHANG, W. QIN, F. ZHAO, Existence and multiplicity of solutions for asymptotically linear nonpreiodic Hamiltonian elliptic system, J. Math. Anal. Appl., 399 (2013), 433-441.
  • W. M. ZOU, M. SCHECHETER, Critical point theory and its applications, Springer, New York (2006).
There are 20 citations in total.

Details

Journal Section Articles
Authors

Mohsen Alimohammady This is me

Morteza Koozehgar Kalleji This is me

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 2

Cite

APA Alimohammady, M., & Kalleji, M. K. (2014). Infinitely many large energy solutions of nonlinear Schr$\ddot{o}$dinger-Maxwell system. New Trends in Mathematical Sciences, 2(2), 87-94.
AMA Alimohammady M, Kalleji MK. Infinitely many large energy solutions of nonlinear Schr$\ddot{o}$dinger-Maxwell system. New Trends in Mathematical Sciences. August 2014;2(2):87-94.
Chicago Alimohammady, Mohsen, and Morteza Koozehgar Kalleji. “Infinitely Many Large Energy Solutions of Nonlinear Schr$\ddot{o}$dinger-Maxwell System”. New Trends in Mathematical Sciences 2, no. 2 (August 2014): 87-94.
EndNote Alimohammady M, Kalleji MK (August 1, 2014) Infinitely many large energy solutions of nonlinear Schr$\ddot{o}$dinger-Maxwell system. New Trends in Mathematical Sciences 2 2 87–94.
IEEE M. Alimohammady and M. K. Kalleji, “Infinitely many large energy solutions of nonlinear Schr$\ddot{o}$dinger-Maxwell system”, New Trends in Mathematical Sciences, vol. 2, no. 2, pp. 87–94, 2014.
ISNAD Alimohammady, Mohsen - Kalleji, Morteza Koozehgar. “Infinitely Many Large Energy Solutions of Nonlinear Schr$\ddot{o}$dinger-Maxwell System”. New Trends in Mathematical Sciences 2/2 (August 2014), 87-94.
JAMA Alimohammady M, Kalleji MK. Infinitely many large energy solutions of nonlinear Schr$\ddot{o}$dinger-Maxwell system. New Trends in Mathematical Sciences. 2014;2:87–94.
MLA Alimohammady, Mohsen and Morteza Koozehgar Kalleji. “Infinitely Many Large Energy Solutions of Nonlinear Schr$\ddot{o}$dinger-Maxwell System”. New Trends in Mathematical Sciences, vol. 2, no. 2, 2014, pp. 87-94.
Vancouver Alimohammady M, Kalleji MK. Infinitely many large energy solutions of nonlinear Schr$\ddot{o}$dinger-Maxwell system. New Trends in Mathematical Sciences. 2014;2(2):87-94.