Concentration for a biharmonic Schrödinger equation
The paper deals with the nonlinear stationary biharmonic Schrödinger equation \[ \begin{cases} \varepsilon^4 \Delta^2u+V(x)u=P(x)f(|u|)u, & x\in \mathbb{R}^N,\\ u(x)\to 0, & \text{as}\;|x|\to\infty, \end{cases} \] where \(\varepsilon\) stands for the Planck constant, and \(V\) and \(P\) are spatial distributions of external potentials. By means of variational methods, the author describes concentration phenomena for the solutions when \(\varepsilon\to0.\)
nonlinear biharmonic Schrödinger equation
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