On the one-dimensional \(p\)-Laplacian with a singular nonlinearity (Q417765)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the one-dimensional \(p\)-Laplacian with a singular nonlinearity |
scientific article; zbMATH DE number 6034701
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the one-dimensional \(p\)-Laplacian with a singular nonlinearity |
scientific article; zbMATH DE number 6034701 |
Statements
On the one-dimensional \(p\)-Laplacian with a singular nonlinearity (English)
0 references
14 May 2012
0 references
\(p\)-Laplacian
0 references
singularity
0 references
positive solution
0 references
existence
0 references
non-existence
0 references
0 references
0 references
0 references
0 references
0 references
0 references
The authors study the existence and non-existence of positive solutions for the \(p\)-Laplacian equation NEWLINE\[NEWLINE (\Phi_p(u'))'-h(t,u)|u'|^p+f(t,u,u')=0,\quad0<t<1,NEWLINE\]NEWLINE with either the boundary conditions NEWLINE\[NEWLINEu(0)=u(1)=0NEWLINE\]NEWLINE or NEWLINE\[NEWLINEu(0)=u(1)=u'(0)=u'(1)=0,NEWLINE\]NEWLINE where \(\Phi_p(s)=|s|^{p-2}s\), \(p>1\) and the nonlinearity \(h\) is allowed to be singular.NEWLINENEWLINEThe methodology involves regularization techniques for the existence results and Gronwall's inequality, an embedding inequality and scaling techniques for the non-existence results.
0 references
