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Nontrivial solutions for the nonlinear biharmonic system with dirichlet boundary condition

정택선|최규흥
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2010.12|한국수학논문집 (Korean Journal of Mathematics)|제18권 제4호|pp. 473-487

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키워드

biharmonic equationlinking theorembiharmonic system
주제분류수학

초록

We investigate the existence of multiple nontrivial so-lutions (ξ,η) for perturbations g1, g2 of the harmonic system with Dirichlet boundary condition Δ2ξ + cΔξ = g1(2ξ + 3η) in ­ΩΔ2η + cΔη = g2(2ξ + 3η) in Ωwhere we assume that λ1 < c < λ2, g'1 (∞), g'2 (∞) are finite. We prove that the system has at least three solutions under some con-dition on g.

Abstract

We investigate the existence of multiple nontrivial so-lutions (ξ,η) for perturbations g1, g2 of the harmonic system with Dirichlet boundary condition Δ2ξ + cΔξ = g1(2ξ + 3η) in ­ΩΔ2η + cΔη = g2(2ξ + 3η) in Ωwhere we assume that λ1 < c < λ2, g'1 (∞), g'2 (∞) are finite. We prove that the system has at least three solutions under some con-dition on g.

참고문헌 (13)

  1. H. Amann, "A note on the degree theory for gradient mappings", Proc. Amer. Math. Soc., 통권 : 85, pp.591~595 (1982)
  2. A. Ambrosetti, "Dual variational methods in critical point theory", J. Funct. Anal., 14, pp.343~381 (1973)
  3. K.C. Chang, "Infinite dimensional Morse theory and multiple solution problems" (1993), BirkhÄauser
  4. R. Chiappinelli, "Bifurcation from infinity and multiple solutions for an elliptic system", Differential Integral Equations, 6, pp.757~771 (1993)
  5. Q.H. Choi, "An application of a variational linking theorem to a nonlinear biharmonic equation", Nonlinear Anal., 47, pp.3695~3705 (2001)
  6. Q.H. Choi, "Multiplicity of solutions and source terms in a fourth order nonlinear elliptic equation", Acta Math. Sci. Ser., 19(4), pp.361~374 (1999)
  7. Q.H. Choi, "Multiplicity results on a fourth order nonlinear elliptic equation", Rocky Mountain J. Math., 29, pp.141~164 (1999)
  8. 정택선, "On the existence of the third solution of the nonlinear biharmonic equation with dirihlet boundary condition", 충청수학회지, 20(1), pp.81~94 (2007), 충청수학회
  9. A.C. Lazer, "Large amplitude periodic oscillations in sus-pension bridge: some new connections with nonlinear analysis", SIAM Rev., 32, pp.537~578 (1990)
  10. A. Marino, "Some variational theorems of mixed type and elliptic problem with jumping nonlinearities", Ann. Sc. Norm. Super. Pisa Cl. Sci., 25, pp.631~665 (1997)
  11. P.J. McKenna, "Travelling waves in a suspension bridge", SIAM J. Appl. Math., 50, pp.703~715 (1990)
  12. P.H. Rabinowitz, "Minimax methods in critical point theory with applications to differential equations", CBMS Reg. Conf. Ser. Math. Amer. Math. Soc., 통권 : 65 (1986)
  13. G.Tarantello, "A note on a semilinear elliptic problem", Differential and Integral Equations, 5, pp.561~566 (1992)

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