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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 10
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Articles

Ground states for a class of asymptotically linear fourth-order elliptic equations

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Pages 2168-2174 | Received 17 Jun 2014, Accepted 20 Oct 2014, Published online: 07 Nov 2014

References

  • Alexiades V, Elcrat AR, Schaefer PW. Existence theorems for some nonlinear fourth-order elliptic boundary value problems. Nonlinear Anal. 1980;4:805–813.
  • An Y, Liu R. Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation. Nonlinear Anal. 2008;68:3325–3331.
  • Ayed MB, Hammami M. On a fourth-order elliptic equation with critical nonlinearity in dimension six. Nonlinear Anal. 2006;64:924–957.
  • Benalili M. Multiplicity of solutions for a fourth-order elliptic equation with critical exponent on compact manifolds. Appl. Math. Lett. 2007;20:232–237.
  • Yang Y, Zhang JH. Existence of solutions for some fourth-order nonlinear elliptical equations. J. Math. Anal. Appl. 2009;351:128–137.
  • Yin YL, Wu X. High energy solutions and nontrivial solutions for fourth-order elliptic equations. J. Math. Anal. Appl. 2011;375:699–705.
  • Liu J, Chen SX, Wu X. Existence and multiplicity of solutions for a class of fourth-order elliptic equations in ℝN. J. Math. Anal. Appl. 2012;395:608–615.
  • Tang XH. New condition on nonlinearity for a periodic Schrödinger equation having zero as spectrum. J. Math. Anal. Appl. 2014;413:392–410.
  • Tang XH. New super-quadratic conditions on ground state solutions for superlinear Schrödinger equation. Adv. Nonlinear Stud. 2014;14:361–373.
  • Ye YW, Tang CL. Infinitely many solutions for fourth-order elliptic equations. J. Math. Anal. Appl. 2012;394:841–854.
  • Ye YW, Tang CL. Existence and multiplicity of solutions for fourth-order elliptic equations in ℝN. J. Math. Anal. Appl. 2013;406:335–351.
  • Zhang W, Tang XH, Zhang J. Infinitely many solutions for fourth-order elliptic equations with general potentials. J. Math. Anal. Appl. 2013;407:359–368.
  • Zhang W, Tang XH, Zhang J. Infinitely many solutions for fourth-order elliptic equations with sign-changing potential. Taiwan. J. Math. 2014;18:645–659.
  • Chang XJ. Ground state solutions of asymptotically linear fractional Schrödinger equations. J. Math. Phys. 2013;54:061504.
  • Zou WM, Schechter M. Critical point theory and its applications. New York (NY): Springer; 2006.

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