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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three dimensional subspace with three axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.
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참고문헌 (10)
참고문헌 신청
A.C. Lazer / 1985 / Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems / J. Math. Anal. Appl 107 : 3719 ~ 3395
A.C. Lazer / 1994 / Global bifurcation and a theorem of Tarantello / J. Math. Anal. Appl 181 : 648 ~ 655
A.M. Micheletti / 1998 / Multiplicity results for a fourth-order semilinear elliptic problem / Nonlinear Anal. TMA 31 : 895 ~ 908
A.M. Micheletti / 1998 / Nontrivial solutions for some fourth order semi- linear elliptic problems / Nonlinear Anal. TMA 34 : 509 ~ 523
P.J. McKenna / 1984 / On the multiplicity of the solution set of some nonlinear boundary value problems / Nonlinear Anal. TMA 8 (8) : 893 ~ 907
A.C. Lazer / 1994 / Global bifurcation and a theorem of Tarantello / J. Math. Anal. Appl 181 : 648 ~ 655
A.M. Micheletti / 1998 / Multiplicity results for a fourth-order semilinear elliptic problem / Nonlinear Anal. TMA 31 : 895 ~ 908
A.M. Micheletti / 1998 / Nontrivial solutions for some fourth order semi- linear elliptic problems / Nonlinear Anal. TMA 34 : 509 ~ 523
P.J. McKenna / 1984 / On the multiplicity of the solution set of some nonlinear boundary value problems / Nonlinear Anal. TMA 8 (8) : 893 ~ 907
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