Boundary eigencurve problems involving the p-Laplacian operator
In this paper, we show that for each $lambda in mathbb{R}$, there is an increasing sequence of eigenvalues for the nonlinear boundary-value problem $$displaylines{ Delta_pu=|u|^{p-2}u quad hbox{in } Omegacr | abla u|^{p-2}frac{partial u}{partial u}=lambda ho(x)|u|^{p-2}u+mu|u|^{p-2}u quad...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2008-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2008/78/abstr.html |
| Summary: | In this paper, we show that for each $lambda in mathbb{R}$, there is an increasing sequence of eigenvalues for the nonlinear boundary-value problem $$displaylines{ Delta_pu=|u|^{p-2}u quad hbox{in } Omegacr | abla u|^{p-2}frac{partial u}{partial u}=lambda ho(x)|u|^{p-2}u+mu|u|^{p-2}u quad hbox{on } partial Omega,; }$$ also we show that the first eigenvalue is simple and isolated. Some results about their variation, density, and continuous dependence on the parameter $lambda$ are obtained. |
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| ISSN: | 1072-6691 |