Three solutions for singular p-Laplacian type equations
In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(|x|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2008-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2008/61/abstr.html |
| Summary: | In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(|x|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property. |
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| ISSN: | 1072-6691 |