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

Yıl 2014, Cilt: 2 Sayı: 2, 87 - 94, 01.08.2014

Öz

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

Kaynakça

  • 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

Yıl 2014, Cilt: 2 Sayı: 2, 87 - 94, 01.08.2014

Öz

Kaynakça

  • 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).
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Yazarlar

Mohsen Alimohammady Bu kişi benim

Morteza Koozehgar Kalleji Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 2 Sayı: 2

Kaynak Göster

APA Alimohammady, M., & Kalleji, M. K. (2014). Infinitely many large energy solutions of nonlinear Schrödinger. New Trends in Mathematical Sciences, 2(2), 87-94.
AMA Alimohammady M, Kalleji MK. Infinitely many large energy solutions of nonlinear Schrödinger. New Trends in Mathematical Sciences. Ağustos 2014;2(2):87-94.
Chicago Alimohammady, Mohsen, ve Morteza Koozehgar Kalleji. “Infinitely many large energy solutions of nonlinear Schrödinger”. New Trends in Mathematical Sciences 2, sy. 2 (Ağustos 2014): 87-94.
EndNote Alimohammady M, Kalleji MK (01 Ağustos 2014) Infinitely many large energy solutions of nonlinear Schrödinger. New Trends in Mathematical Sciences 2 2 87–94.
IEEE M. Alimohammady ve M. K. Kalleji, “Infinitely many large energy solutions of nonlinear Schrödinger”, New Trends in Mathematical Sciences, c. 2, sy. 2, ss. 87–94, 2014.
ISNAD Alimohammady, Mohsen - Kalleji, Morteza Koozehgar. “Infinitely many large energy solutions of nonlinear Schrödinger”. New Trends in Mathematical Sciences 2/2 (Ağustos2014), 87-94.
JAMA Alimohammady M, Kalleji MK. Infinitely many large energy solutions of nonlinear Schrödinger. New Trends in Mathematical Sciences. 2014;2:87–94.
MLA Alimohammady, Mohsen ve Morteza Koozehgar Kalleji. “Infinitely many large energy solutions of nonlinear Schrödinger”. New Trends in Mathematical Sciences, c. 2, sy. 2, 2014, ss. 87-94.
Vancouver Alimohammady M, Kalleji MK. Infinitely many large energy solutions of nonlinear Schrödinger. New Trends in Mathematical Sciences. 2014;2(2):87-94.