One-dimensional elliptic equation with concave and convex nonlinearities
We establish the exact number of positive solutions for the boundary-value problem $$displaylines{ -(|u'|^{m-2} u')'=lambda u^q + u^pquad hbox{in }(0,1)cr u(0)= u(1)=0,, }$$ where $0leq q < m- 1 < p$ and $lambda$ is positive.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2000-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/50/abstr.html |
| Summary: | We establish the exact number of positive solutions for the boundary-value problem $$displaylines{ -(|u'|^{m-2} u')'=lambda u^q + u^pquad hbox{in }(0,1)cr u(0)= u(1)=0,, }$$ where $0leq q < m- 1 < p$ and $lambda$ is positive. |
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| ISSN: | 1072-6691 |