Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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AN APPLICATION OF A LINKING METHOD TO A GENERAL ELLIPTIC SYSTEM

  • Nam, Hyewon (Department of General Education Namseoul University)
  • Received : 2010.01.10
  • Accepted : 2010.03.10
  • Published : 2010.03.01
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Abstract

In this work, we consider an elliptic system of three equations in dimension greater than one. We prove that the system has at least three nontrivial solutions by applying a linking theorem.

Keywords

References

  1. A.M. Micheletti, C. Saccon, Multiple solutions for an asymptotically linear problem in $R^N$. Nonlinear Anal., 56 (2004), no. 1, 1-18. https://doi.org/10.1016/j.na.2003.04.001
  2. A. Szulkin, Critical point theory of Ljusterni-Schnirelmann type and applications to partial differential equations. Sem. Math. Sup., Vol. 107, pp. 35-96, Presses Univ. Montreal, Montreal, QC, 1989.
  3. D. Lupo, A.M. Micheletti, Two applications of a three critical points theorem. J. Differential Equations, 132 (1996), no. 2, 222-238. https://doi.org/10.1006/jdeq.1996.0178
  4. Evans, Lawrence C., Partial differential equations. American Mathematical Society, (1998).
  5. Jin Yinghua, Nontrivial solutions of nonlinear elliptic equations and elliptic systems. Inha U. 2004.
  6. Zou, Wenming, Multiple solutions for asymptotically linear elliptic systems. J. Math. Anal. Appl., 255 (2001), no. 1, 213-229. https://doi.org/10.1006/jmaa.2000.7236