Existence results for semilinear elliptic equations with some lack of coercivity
Published online by Cambridge University Press: 14 July 2008
Abstract
We consider the following problem:
\begin{alignat*}{2} -\text{div}(A(x,u)\nabla u)&=u^s+f(x) & \quad &\text{in }\varOmega, \\ u(x)&\ge0 & & \text{in }\varOmega, \\ u(x)&=0 & & \text{on }\p\varOmega, \end{alignat*}
where $\varOmega$ is an open bounded subset of $\mathbb{R}^N$, $N\ge3$, and
$$ A:\varOmega\times\mathbb{R}\rightarrow M_{N\times N} $$
is an elliptic matrix such that when $u\to\infty$ is non-coercive.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 3 , June 2008 , pp. 569 - 595
- Copyright
- 2008 Royal Society of Edinburgh
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