Nonautonomous and non periodic Schrödinger equation with indefinite linear part
Journal of Fixed Point Theory and Applications, 2017•Springer
The existence of solution of the nonlinear Schrödinger equation-Δ u+ V (x) u= f (x, u), &-Δ u+
V (x) u= f (x, u), is stablished in R^ N RN, where V changes sign and f is an asymptotically
linear function at infinity, with V and f non periodic in x. Spectral theory, a classical linking
theorem and interaction between translated solutions of the problem at infinity are
employed.
V (x) u= f (x, u), is stablished in R^ N RN, where V changes sign and f is an asymptotically
linear function at infinity, with V and f non periodic in x. Spectral theory, a classical linking
theorem and interaction between translated solutions of the problem at infinity are
employed.
Abstract
The existence of solution of the nonlinear Schrödinger equation $$\begin{aligned} \begin{array}{lc} -\Delta u + V(x) u = f(x,u),&\end{array} \end{aligned}$$is stablished in , where V changes sign and f is an asymptotically linear function at infinity, with V and f non periodic in x. Spectral theory, a classical linking theorem and interaction between translated solutions of the problem at infinity are employed.
Springer
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