** Laure Cardoulis**

**Existence of Solutions for an Elliptic Equation Involving a Schrödinger Operator with Weight in all of the Space **

**The paper is published:**
Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 58, 53-65(2004)

**MSC:**- 35J10 Schrodinger operator, See also {35Pxx}

**Abstract:** In this paper, we obtain some results about the existence of

solutions for the following elliptic semilinear equation $(-\Delta

+q)u = \lambda mu+f(x,u) \mbox{ in } \mathbb{R}^{N}$ where $q$ is a positive

potential satisfying $\lim_{\vert x \vert \rightarrow + \infty}q(x )= +\infty$

and $m$ is a bounded positive weight.

**Keywords:** *Schrodinger operator*