Abstract and Applied Analysis

Multiplicity of Solutions for Neumann Problems for Semilinear Elliptic Equations

Yu-Cheng An and Hong-Min Suo

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Abstract

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of Neumann problems in the case near resonance. The results improve and generalize some of the corresponding existing results.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 360581, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277023

Digital Object Identifier
doi:10.1155/2014/360581

Mathematical Reviews number (MathSciNet)
MR3216044

Zentralblatt MATH identifier
07022222

Citation

An, Yu-Cheng; Suo, Hong-Min. Multiplicity of Solutions for Neumann Problems for Semilinear Elliptic Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 360581, 11 pages. doi:10.1155/2014/360581. https://projecteuclid.org/euclid.aaa/1412277023


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References

  • C. Li, “The existence of infinitely many solutions of a class of nonlinear elliptic equations with Neumann boundary condition for both resonance and oscillation problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 54, no. 3, pp. 431–443, 2003.
  • A. Qian, “Existence of infinitely many nodal solutions for a superlinear Neumann boundary value problem,” Boundary Value Problems, vol. 2005, no. 3, pp. 329–335, 2005.
  • D. Motreanu, D. O'Regan, and N. S. Papageorgiou, “A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems,” Communications on Pure and Applied Analysis, vol. 10, no. 6, pp. 1791–1816, 2011.
  • C.-L. Tang and X.-P. Wu, “Existence and multiplicity for solutions of Neumann problem for semilinear elliptic equations,” Journal of Mathematical Analysis and Applications, vol. 288, no. 2, pp. 660–670, 2003.
  • D. Motreanu, V. V. Motreanu, and N. S. Papageorgiou, Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, Springer, New York, NY, USA, 2014.
  • L. Gasiński and N. S. Papageorgiou, “Multiplicity of solutions for Neumann problems with an indefinite and unbounded potential,” Communications on Pure and Applied Analysis, vol. 12, no. 5, pp. 1985–1999, 2013.
  • N. S. Papageorgiou and V. D. Rădulescu, “Semilinear Neumann problems with indefinite and unbounded potential and crossing nonlinearity,” in Recent trends in Nonlinear Partial Differential Equations. II. Stationary Problems, vol. 595 of Contemporary Mathematics, pp. 293–315, American Mathematical Society, Providence, RI, USA, 2013.
  • J. Mawhin and K. Schmitt, “Nonlinear eigenvalue problems with the parameter near resonance,” Annales Polonici Mathematici, vol. 51, pp. 241–248, 1990.
  • T. F. Ma, M. Ramos, and L. Sanchez, “Multiple solutions for a class of nonlinear boundary value problems near resonance: a variational approach,” Nonlinear Analysis: Theory, Methods & Applications, vol. 30, no. 6, pp. 3301–3311, 1997.
  • T. F. Ma and M. L. Pelicer, “Perturbations near resonance for the $p$-laplacian in ${\mathbb{R}}^{N}$,” Abstract and Applied Analysis, vol. 7, no. 6, pp. 323–334, 2002.
  • T. F. Ma and L. Sanchez, “Three solutions of a quasilinear elliptic problem near resonance,” Mathematica Slovaca, vol. 47, no. 4, pp. 451–457, 1997.
  • Z.-Q. Ou and C.-L. Tang, “Existence and multiplicity results for some elliptic systems at resonance,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2660–2666, 2009.
  • F. O. de Paiva and E. Massa, “Semilinear elliptic problems near resonance with a nonprincipal eigenvalue,” Journal of Mathematical Analysis and Applications, vol. 342, no. 1, pp. 638–650, 2008.
  • H.-M. Suo and C.-L. Tang, “Degenerate semilinear elliptic problems near resonance with a nonprincipal eigenvalue,” Bulletin of the Korean Mathematical Society, vol. 49, no. 4, pp. 669–684, 2012.
  • L. C. Evance, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, USA, 1998.
  • A. Marino, A. M. Micheletti, and A. Pistoia, “A nonsymmetric asymptotically linear elliptic problem,” Topological Methods in Nonlinear Analysis, vol. 4, no. 2, pp. 289–339, 1994.
  • P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol. 65 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, USA, 1986.
  • C.-L. Tang and X.-P. Wu, “Periodic solutions for second order systems with not uniformly coercive potential,” Journal of Mathematical Analysis and Applications, vol. 259, no. 2, pp. 386–397, 2001. \endinput