Laure Cardoulis
Existence of solutions for some semilinear elliptic systems
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. [56], [29]-[38]([2002])
MSC:
35-XX Partial differential equations
Abstract: We obtain results on the existence of solutions for the semilinear
elliptic equation $(-\Delta +q)u=\lambda \rho u+f(x,u)$ in $\Rset^{N}$ under
the hypothesis that $N\geq 3,\; q(x)\to +\infty\quad\mbox{as}\quad |x|\to +\infty$ and $\rho \in L^{\frac{N}{2}}(\Rset^{N}).$
Similar results for semilinear systems of $n$ equations are also established.

Keywords: Partial differential equations