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We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the
Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.
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참고문헌 (14)
참고문헌 신청
.C. Lazer / 1994 / Global bifurcation and a theorem of Tarantello / J.Math. Anal. Appl., 181 : 648 ~ 655
A. C. Lazer / 1985 / Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems / J. Math. Anal. Appl 107 : 371 ~ 395
A. M. Micheletti / 1998 / Multiplicity results for a fourth-order semilinear elliptic problem / Nonlinear Analysis TMA 31 : 895 ~ 908
A. M. Micheletti / 1998 / Nontrivial solutions for some fourth order semilinear elliptic problems / Nonlinear Analysis 34 : 509 ~ 523
G. Tarantello / 1992 / A note on a semilinear elliptic problem / Diff. Integ. Equations : 561 ~ 565
A. C. Lazer / 1985 / Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems / J. Math. Anal. Appl 107 : 371 ~ 395
A. M. Micheletti / 1998 / Multiplicity results for a fourth-order semilinear elliptic problem / Nonlinear Analysis TMA 31 : 895 ~ 908
A. M. Micheletti / 1998 / Nontrivial solutions for some fourth order semilinear elliptic problems / Nonlinear Analysis 34 : 509 ~ 523
G. Tarantello / 1992 / A note on a semilinear elliptic problem / Diff. Integ. Equations : 561 ~ 565
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