Abstract: 
This talk is concerned with the existence of solutions to the nonlinear Schr\{o}dinger equation $\Delta u + V(x) u = \lambda f(u)$ in $\mathbf{R}^N$. Here $\lambda > 0$ is a parameter and we only require the nonlinearity $f$ to satisfy conditions around $0$. Our results are the existence of positive solutions when $\lambda$ is sufficiently large and the asymptotic behavior of positive solutions as $\lambda \to \infty$. This is joint work with Shinji Adachi (Shizuoka University) and Tatsuya Watanabe (Kyoto Sangyo University). 
