No CrossRef data available.
Article contents
Existence and L∞ estimates of some Mountain-Pass type solutions
Published online by Cambridge University Press: 02 July 2009
Abstract
We prove the existence of a positive solution to the BVP
$$(\Phi(t)u'(t))'=f(t,u(t)),\,\,\,\,\,\,\,\,\,\,\,u'(0)=u(1)=0, $$
imposing some conditions on Φ and f. In particular, we
assume $\Phi(t)f(t,u)$
to be decreasing in t. Our method
combines variational and topological arguments and can be applied
to some elliptic problems in annular domains. An $L_\infty$
bound
for the solution is provided by the $L_\infty$
norm of any test
function with negative energy.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 3 , July 2009 , pp. 499 - 508
- Copyright
- © EDP Sciences, SMAI, 2009
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20161010014056333-0747:S1292811909000153:S1292811909000153_eqnU6.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20161010014056333-0747:S1292811909000153:S1292811909000153_eqnU1.gif?pub-status=live)