Eigenvalue problems of nonhomogeneous semilinear elliptic equations in Esteban–Lions domains with holes |
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Authors: | Tsing-San Hsu Huei-Li Lin |
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Institution: | aCenter for General Education, Chang Gung University, Kwei-San, Tao-Yuan 333, Taiwan |
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Abstract: | In this article, we consider the following eigenvalue problems where λ>0, N2 and is the upper semi-strip domain with a hole in . Under some suitable conditions on f and h, we show that there exists a positive constant λ* such that Eq. (*)λ has at least two solutions if λ(0,λ*), a unique positive solution if λ=λ*, and no positive solution if λ>λ*. We also obtain some further properties of the positive solutions of (*)λ. |
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Keywords: | Eigenvalue problems Nonhomogeneous semilinear elliptic equation Esteban– Lions domains |
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