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초록· 키워드
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We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator -△. We prove this result by investigating the Lipschitz
constant of the inverse compact operator of Dt -△ and applying
the contraction mapping principle.
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참고문헌 (16)
참고문헌 신청
A. Ambrosetti / 1973 / On the inversion of some di®erentiable map- pings with singularities between Banach spaces / Annali Mat.pura appl 93 : 231 ~ 247
A. C. Lazer / 1981 / On the number of solutions of a nonlinear Dirichlet problem / J. Math. Analysis Applic 84 : 282 ~ 294
C. L. Dolph / 1949 / Nonlinear integral equations of the Hammerstein type / Trans. Am. math.Soc 60 : 289 ~ 307
E. N. Dancer / 1978 / On the ranges of certain weakly nonlinear elliptic partial di®er- ential equations / J. Math. pures appl 57 : 351 ~ 366
H. Amann / 1979 / A multiplicity result for a class of elliptic boundary value problems / Proc. R. Soc. Edinb. 84-A : 145 ~ 151
A. C. Lazer / 1981 / On the number of solutions of a nonlinear Dirichlet problem / J. Math. Analysis Applic 84 : 282 ~ 294
C. L. Dolph / 1949 / Nonlinear integral equations of the Hammerstein type / Trans. Am. math.Soc 60 : 289 ~ 307
E. N. Dancer / 1978 / On the ranges of certain weakly nonlinear elliptic partial di®er- ential equations / J. Math. pures appl 57 : 351 ~ 366
H. Amann / 1979 / A multiplicity result for a class of elliptic boundary value problems / Proc. R. Soc. Edinb. 84-A : 145 ~ 151
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