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A bifurcation problem for the biharmonic operator

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주제분류수학

초록

We investigate the number of the solutions for the biharmonic boundary value problem with a variable coefficient nonlinear term. We get a theorem which shows the existence of $m$ weak solutions for the biharmonic problem with variable coefficient. We obtain this result by using the critical point theory induced from the invariant function and invariant linear subspace.

Abstract

We investigate the number of the solutions for the biharmonic boundary value problem with a variable coefficient nonlinear term. We get a theorem which shows the existence of $m$ weak solutions for the biharmonic problem with variable coefficient. We obtain this result by using the critical point theory induced from the invariant function and invariant linear subspace.

참고문헌 (9)

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  3. Q.H. Choi, "Multiplicity results on nonlinear biharmonic operator", Rocky Mountain J. Math, 29(1), pp.141~164 (1999)
  4. 이성진, "Almost homomorphisms between Banach algebras", 한국수학논문집, 18(1), pp.1~10 (2010), 강원경기수학회
  5. T.S. Jung, "Multiplicity results on a nonlinear biharmonic equation", Nonlinear Anal, 30(8), pp.5083~5092 (1997)
  6. A.C. Lazer, "Multiplicity results for a class of semilinear elliptic and parabolic boundary value problems", J. Math. Anal. Appl, 107, pp.371~395 (1985)
  7. A.M. Micheletti, "Multiplicity results for a fourth-order semilinear elliptic problem", Nonlinear Anal, 31(7), pp.895~908 (1998)
  8. P.H. Rabinowitz, "Minimax methods in critical point theory with applications to differential equations", CBMS Reg. Conf. Ser. Math., 65, Amer. Math. Soc (1986)
  9. Tarantello, "A note on a semilinear elliptic problem", Differential Integral Equations, 5(3), pp.561~565 (1992)

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