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The nonlinear eigenvalue problem for p-Laplacian $$\left\{\begin{array}{c}-{div\left(a\left(x\right)\right|\nabla u|}^{p-2}{\nabla u)=\lambda g\left(x\right)|u|}^{p-2}u\text{in}{ℝ}^N,u>0\text{in}{ℝ}^N,\underset{\left|x\right|\to \infty }{lim}u\left(x\right)=0,\hfill \end{array}\right.$$ is considered. We assume that $1<p<N$ and that $g$ is indefinite weight function. The existence and $C^{1,\alpha }$-regularity of the weak solution is proved.