Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
The authors establish lower bounds for the number of nodal bound states for the semiclassical nonlinear Schrödinger equation \(-\varepsilon ^{2}\Delta u+a\left( x\right) u=\left| u\right| ^{p-2}u\) in \({\mathbb R}^{N},\) with bounded and uniformly continuous potential \(a.\) The solutions have two nodal domains, and their positive and negative parts concentrate near the set of minimum points of \(a.\) The existence of infinitely many nodal solutions for fixed small \(\varepsilon \) is obtained. Variational techniques and Lusternik-Schnirelman theory are used. The paper provides the lower bounds for the cuplength of the configuration spaces.
scientific article; zbMATH DE number 5162074
scientific article