A Dirichlet problem with asymptotically linear and changing sign nonlinearity. (Q1432787)
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: A Dirichlet problem with asymptotically linear and changing sign nonlinearity. |
scientific article; zbMATH DE number 2076539
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Dirichlet problem with asymptotically linear and changing sign nonlinearity. |
scientific article; zbMATH DE number 2076539 |
Statements
A Dirichlet problem with asymptotically linear and changing sign nonlinearity. (English)
0 references
22 June 2004
0 references
The authors discuss the existence of positive solutions to the problem \[ -\Delta u= g(x, u),\quad u\in H^1_0(\Omega),\tag{1} \] where \(\Omega\) is a bounded domain of \(\mathbb{R}^d\), \(g(x,s)\) is allowed to change sign and has an asymptotically linear behaviour in \(\delta\) at infinity. Using the mountain pass theorem the authors prove existence of solutions for (1).
0 references
elliptic equation
0 references
mountain pass theorem
0 references
asymptotically linear nonlinearity
0 references
