Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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BIFURCATION PROBLEM FOR THE SUPERLINEAR ELLIPTIC OPERATOR

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2012.08.07
  • Accepted : 2012.09.15
  • Published : 2012.09.30
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Abstract

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

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References

  1. K.C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkhauser, (1993).
  2. T. Jung, and Q.H. Choi, Multiple solutions result for the mixed type nonlinear elliptic problem, Korean J. Math. 19 (2011), 423-436. https://doi.org/10.11568/kjm.2011.19.4.423
  3. P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math. 65, Amer. Math. Soc., Providence, Rhode Island (1986).

Cited by

  1. EXISTENCE OF THE SOLUTIONS FOR THE ELLIPTIC PROBLEM WITH NONLINEAR TERM DECAYING AT THE ORIGIN vol.20, pp.4, 2012, https://doi.org/10.11568/kjm.2012.20.4.533