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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 14
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Research Article

Nontrivial solutions for an elliptic system of Hamiltonian type

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Pages 5017-5041 | Received 07 Aug 2020, Accepted 10 Jan 2021, Published online: 27 Jan 2021

References

  • Ding Y. Variational methods for strongly indefinite problems. Singapore: World Scientific; 2007.
  • Bartsch T, Ding Y. Deformation theorems on non-metrizable vector spaces and applications to critical point theory. Math Nachr. 2006;279:1–22.
  • Bartsch T, de Figueiredo DG. Infinitely many solutions of nonlinear elliptic systems. Prog Nonlinear Differ Equ Appl. 1999;35:51–67.
  • Bartsch T, Willem M. Infinitely many nonradial solutions of a Euclidean scalar field equation. J Funct Anal. 1993;117:447–460.
  • Yang J. Nontrivial solutions of semilinear elliptic systems in RN. Electron J Differ Equ. 2001;6:343–357.
  • Zhao F, Zhao L, Ding Y. Multiple solutions for a superlinear and periodic elliptic systems on RN. Z Angew Math Phys. 2011;62:495–511.
  • Shi H, Chen H. Ground state solutions for resonant cooperative elliptic systems with general superlinear terms. Mediterr J Math. 2016;13:2897–2909.
  • Zhu X, Cao D. The concentration-compactness principle in nonlinear elliptic equations. Acta Math Sci. 1989;9:307–328.
  • Szulkin A, Weth T. Ground state solutions for some indefinite variational problems. J Funct Anal. 2009;257:3802–3822.
  • Xia L, Zhang J, Zhao F. Ground state solutions for superlinear elliptic systems on RN. J Math Anal Appl. 2013;401:518–525.
  • Liao F, Tang X, Zhang J. Existence of solutions for periodic elliptic system with general superlinear nonlinearity. Z Angew Math Phys. 2015;66:689–701.
  • Sun J, Chen H, Nieto JJ. Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems. J Math Anal Appl. 2011;373:20–29.
  • Liu Z, Bartsch T, Weth T. Sign changing solutions of superlinear Schrödinger equations. Commun Partial Differ Equ. 2004;(1–2):25–42.
  • Hulshof J, Van Der Vorst R. Differential systems with strongly indefinite variational structure. J Funct Anal. 1993;114:32–58.
  • Saldaña A, Tavares H. Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions. J Differ Equ. 2018;265:6127–6165.
  • Bonheure D, dos Santos EM, Ramos M, et al. Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems. J Math Pures Appl. 2015;104:1075–1107.
  • de Figueiredo DG, Jianfu Y. Decay, symmetry and existence of solutions of semilinear elliptic systems. Nonlinear Anal Theory Method Appl. 1998;33:211–234.
  • I.Ávila A, Yang J. On the existence and shape of least energy solutions for some elliptic systems. J Differ Equ. 2003;191:348–376.
  • Chen P, Liu X. Ground states of linearly coupled systems of Choquard type. Appl Math Lett. 2018;84:70–75.
  • Kryszewski W, Szulkin A. Generalized linking theorem with an application to semilinear Schrödinger equations. Adv Differ Equ. 1998;3:441–472.
  • Wang J, Xu J, Zhang F. Existence of solutions for nonperiodic superquadratic Hamiltonian elliptic systems. Nonlinear Anal. 2010;72:1949–1960.
  • Zhao F, Zhao L, Ding Y. Multiple solutions for asymptotically linear elliptic systems. Nonlinear Differ Equ Appl. 2008;15:673–688.
  • Zhao F, Zhao L, Ding Y. A note on superlinear Hamiltonian elliptic systems. J Math Phys. 2009;50:112702.
  • Ding Y, Lee C. Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system. J Differ Equ. 2009;246:2829–2848.
  • Sun J, Chen H, Nieto JJ, et al. The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects. Nonlinear Anal. 2010;72:4575–4586.
  • Yang M, Chen W, Ding Y. Solutions of a class of Hamiltonian elliptic systems in RN. J Math Anal Appl. 2010;362:338–349.
  • Yang L, Chen H, Sun J. Infinitely many homoclinic solutions for some second order Hamiltonian systems. Nonlinear Anal. 2011;74:6459–6468.
  • Edmunds DE, Evans WD. Spectral theory and differential operators. Oxford: Clarendon; 1987.
  • Chen P, Liu X. Ground states for Kirchhoff equation with Hartree-type nonlinearities. J Math Anal Appl. 2019;473:587–608.
  • Pankov A. Periodic nonlinear Schrödinger equation with application to photonic crystals. Milan J Math. 2005;73:259–287.
  • Willem M. Minimax theorem. Boston (MA): Birkhäuser; 1996.
  • Sun J, Chen H, Nieto JJ. Infinitely many solutions for second-order Hamiltonian system with impulsive effects. Math Comput Model. 2011;54:544–555.
  • Sirakov B. On the existence of solutions of Hamiltonian elliptic systems in RN. Adv Differ Equ. 2000;5:1445–1464.
  • Liu Z, Wang Z. Vector solutions with prescribed component wise nodes for a Schrödinger system. Anal Theory Appl. 2019;35:288–311.
  • Ding Y, Jeanjean L. Homoclinic orbits for nonperiodic Hamiltonian system. J Differ Equ. 2007;237:473–490.
  • Zhang W, Zhang J, Zhao F. Multiple solutions for asymptotically quadratic and superquadratic elliptic system of Hamiltonian type. Appl Math Comput. 2015;263:36–46.
  • Liu Z, Sun J. Invariant sets of descending flow in critical point theory with applications to nonlinear differential equations. J Differ Equ. 2001;172:257–299.
  • Bartsch T, Willem M. Infinitely many radial solutions of a semilinear elliptic problem on RN. Arch Ration Mech Anal. 1993;124:261–276.

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