Existence results for semilinear elliptic equations with some lack of coercivity
Anna Mercaldo, Ireneo Peral · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2008
We consider the following problem:\begin{alignat*}{2} -\text{div}(A(x,u) abla 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 A:\varOmega\times\mathbb{R}\rightarrow M_{N\times N} is non-coercive.