A necessary and sufficient condition for the existence of positive solutions to the singular \(p\)-Laplacian (Q1431148)
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scientific article; zbMATH DE number 2068762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A necessary and sufficient condition for the existence of positive solutions to the singular \(p\)-Laplacian |
scientific article; zbMATH DE number 2068762 |
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A necessary and sufficient condition for the existence of positive solutions to the singular \(p\)-Laplacian (English)
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27 May 2004
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Summary: This paper studies the boundary value problem \[ \bigl(\varphi_p (u')\bigr)'+ q(t)\bigl(f(u)+ g(u)\bigr)=0,\;0<t<1,\;u(0)= u(1)=0, \] in the case \(p>1\). A necessary and sufficient condition for the existence of \(C^1 [0,1]\) positive solutions and a sufficient condition for the existence of \(C[0,1]\) positive solutions are presented.
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